[1] M. Acheritogaray, P. Degond, A. Frouvelle, and J.-G. Liu, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinet. Relat. Models 4 (2011), 901-918.
[2] H. Bae, Global well-posedness of dissipative quasi-geostrophic equations in critical spaces, Proc. Amer. Math. Soc. 136 (2008).
[3] A. Babin, A. Mahalov, and B. Nicolaenko, Regularity and integrability of 3D Euler and NavierStokes equations for rotating fluids, Asymptot. Anal. 15 (1997), no. 2, 103-150.
[4] , Global regularity of 3D rotating Navier-Stokes equations for resonant domains, Appl. Math. Lett. 13 (2000), no. 4, 51-57.
[5] , 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity, Indiana Univ. Math. J. 50 (2001), no. Special Issue, 1-35. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000).
[6] H. Bahouri, J.-Y. Chemin, and R. Danchin, Fourier analysis and nonlinear partial differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 343, Springer, Heidelberg, 2011.
[7] M. J. Benvenutti and L. C. F. Ferreira, Existence and stability of global large strong solutions for the Hall-magnetohydrodynamics system, Differential Integral Equations 29 (2016), 977-1000.
[8] J. L. Bona and R. Smith, The initial-value problem for the Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 555-601.
[9] L. A. Caffarelli and A. Vasseur, Drift diffusion equations with fractional diffusion and the quasigeostrophic equation, Ann. of Math. (2) 171 (2010), 1903–1930.
[10] M. Cannone, C. Miao, and L. Xue, Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing, Proc. Lond. Math. Soc. (3) 106 (2013), 650–674.
[11] J. A. Carrillo and L. C. F. Ferreira, The asymptotic behaviour of subcritical dissipative quasigeostrophic equations, Nonlinearity 21 (2008), 1001–1018.
[12] D. Chae, Local existence and blow-up criterion for the Euler equations in the Besov spaces, Asymptot. Anal. 38 (2004), 339-358.
[13] D. Chae, P. Degond, and J.-G. Liu, Well-posedness for Hall-magnetohydrodynamics, Ann. Inst. H. Poincaré C Anal. Non Linéaire 31 (2014), 555–565.
[14] D. Chae and J. Lee, Global well-posedness in the supercritical dissipative quasi-geostrophic equations, Comm. Math. Phys. 233 (2003), 297–311.
[15] , On the blow-up criterion and small data global existence for the Hallmagnetohydrodynamics, J. Differential Equations 256 (2014), 3835–3858. 201
[16] , On the blow-up criterion and small data global existence for the Hallmagnetohydrodynamics, J. Differential Equations 256 (2014), 3835-3858.
[17] F. Charve and R. Danchin, A global existence result for the compressible Navier-Stokes equations in the critical L p framework, Arch. Ration. Mech. Anal. 198 (2010), no. 1, 233–271.
[18] J.-Y. Chemin, B. Desjardins, I. Gallagher, and E. Grenier, Mathematical geophysics, Oxford Lecture Series in Mathematics and its Applications, vol. 32, The Clarendon Press, Oxford University Press, Oxford, 2006. An introduction to rotating fluids and the Navier-Stokes equations.
[19] J.-Y. Chemin and N. Lerner, Flot de champs de vecteurs non lipschitziens et équations de NavierStokes, J. Differential Equations 121 (1995), 314-328 (French).
[20] J.-Y. Chemin and P. Zhang, On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations, Comm. Math. Phys. 272 (2007), 529–566.
[21] J. Chen and Z.-M. Chen, Commutator estimate in terms of partial derivatives of solutions for the dissipative quasi-geostrophic equation, Vol. 444, 2016.
[22] Q. Chen, C. Miao, and Z. Zhang, A new Bernstein’s inequality and the 2D dissipative quasigeostrophic equation, Comm. Math. Phys. 271 (2007).
[23] , Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities, Rev. Mat. Iberoam. 26 (2010), 915-946.
[24] , On the well-posedness of the ideal magnetohydrodynamics equations in the Triebel-Lizorkin spaces, Arch. Ration. Mech. Anal. 195 (2010), 561-578.
[25] , On the ill-posedness of the compressible Navier-Stokes equations in the critical Besov spaces, Rev. Mat. Iberoam. 31 (2015), no. 4, 1375–1402.
[26] Q. Chen and Z. Zhang, Global well-posedness of the 2D critical dissipative quasi-geostrophic equation in the Triebel-Lizorkin spaces, Nonlinear Anal. 67 (2007), 1715-1725.
[27] M. Cheng, Time-periodic and stationary solutions to the compressible Hall-magnetohydrodynamic system, Z. Angew. Math. Phys. 68 (2017), Paper No. 38, 24.
[28] N. Chikami, On Gagliardo-Nirenberg type inequalities in Fourier-Herz spaces, J. Funct. Anal. 275 (2018), 1138–1172.
[29] H. J. Choe and B. J. Jin, Weighted estimate of the asymptotic profiles of the Navier-Stokes flow in R n, J. Math. Anal. Appl. 344 (2008), 353–366.
[30] P. Constantin and V. Vicol, Nonlinear maximum principles for dissipative linear nonlocal operators and applications, Geom. Funct. Anal. 22 (2012), 1289-1321.
[31] P. Constantin and J. Wu, Behavior of solutions of 2D quasi-geostrophic equations, SIAM J. Math. Anal. 30 (1999), 937-948.
[32] B. Cushman-Roisin and J.-M. Beckers, Introduction to geophysical fluid dynamics: physical and numerical aspects, Academic press, 2011.
[33] M. Coti Zelati and V. Vicol, On the global regularity for the supercritical SQG equation, Indiana Univ. Math. J. 65 (2016), 535–552.
[34] R. Danchin, Global existence in critical spaces for compressible Navier-Stokes equations, Invent. Math. 141 (2000), 579–614.
[35] , A Lagrangian approach for the compressible Navier-Stokes equations, Ann. Inst. Fourier (Grenoble) 64 (2014), no. 2, 753-791 (English, with English and French summaries).
[36] R. Danchin and J. Tan, On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces, Comm. Partial Differential Equations 46 (2021), 31–65.
[37] , The Global Solvability Of The Hall-magnetohydrodynamics System In Critical Sobolev Spaces, arXiv:1912.09194.
[38] M. F. de Almeida, L. C. F. Ferreira, and L. S. M. Lima, Uniform global well-posedness of the Navier-Stokes-Coriolis system in a new critical space, Math. Z. 287 (2017), no. 3-4, 735-750.
[39] T. M. Elgindi and K. Widmayer, Sharp decay estimates for an anisotropic linear semigroup and applications to the surface quasi-geostrophic and inviscid Boussinesq systems, SIAM J. Math. Anal. 47 (2015), 4672-4684.
[40] M. Escobedo and E. Zuazua, Large time behavior for convection-diffusion equations in RN , J. Funct. Anal. 100 (1991), 119–161.
[41] F. Fanelli, Incompressible and fast rotation limit for barotropic Navier-Stokes equations at large Mach numbers, Phys. D 428 (2021), chapter No. 133049, 20.
[42] D. Fang, B. Han, and M. Hieber, Local and global existence results for the Navier-Stokes equations in the rotational framework, Commun. Pure Appl. Anal. 14 (2015), no. 2, 609-622.
[43] E. Feireisl, I. Gallagher, D. Gerard-Varet, and A. Novotný, Multi-scale analysis of compressible viscous and rotating fluids, Comm. Math. Phys. 314 (2012), no. 3, 641-670.
[44] E. Feireisl, I. Gallagher, and A. Novotný, A singular limit for compressible rotating fluids, SIAM J. Math. Anal. 44 (2012), no. 1, 192-205.
[45] E. Feireisl and A. Novotný, Multiple scales and singular limits for compressible rotating fluids with general initial data, Comm. Partial Differential Equations 39 (2014), no. 6, 1104-1127.
[46] Y. Fujigaki and T. Miyakawa, Asymptotic profiles of nonstationary incompressible Navier-Stokes flows in the whole space, SIAM J. Math. Anal. 33 (2001), 523–544.
[47] M. Fujii, Long time existence and asymptotic behavior of solutions for the 2d quasi-geostrophic equation with large dispersive forcing, J. Math. Fluid Mech. 23 (2021), Paper No. 12, 19.
[48] , Large time behavior of solutions to the 3D anisotropic Navier-Stokes equation, arXiv:2108.11940, accepted.
[49] , Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation, J. Evol. Equ. 22 (2022), Paper No. 24, 29.
[50] , Global solutions to the dissipative quasi-geostrophic equation with dispersive forcing, J. Math. Soc. Japan (2022).
[51] , Global well-posedness of the incompressible Hall-magnetohydrodynamics system in large critical spaces, preprint.
[52] , Global solutions to the Navier-Stokes-Coriolis equation with large data in the critical Fourier-Besov spaces, preprint.
[53] M. Fujii and R. Nakasato, Global solutions for the incompressible Hall-magnetohydrodynamics system around constant equilibrium states, preprint.
[54] M. Fujii and K. Watanabe, Compressible Navier-Stokes-Coriolis system in critical Besov spaces, preprint.
[55] H. Fujita and T. Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16 (1964), 269-315. 203
[56] M. Geissert, M. Hieber, and T. H. Nguyen, A general approach to time periodic incompressible viscous fluid flow problems, Arch. Ration. Mech. Anal. 220 (2016), 1095–1118.
[57] Y. Giga, K. Inui, A. Mahalov, and J. Saal, Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data, Indiana Univ. Math. J. 57 (2008), no. 6, 2775-2791.
[58] A. Grünrock, An improved local well-posedness result for the modified KdV equation, Int. Math. Res. Not. (2004), 3287-3308.
[59] B. Haspot, Existence of global strong solutions in critical spaces for barotropic viscous fluids, Arch. Ration. Mech. Anal. 202 (2011), no. 2, 427–460.
[60] M. Hieber and Y. Shibata, The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework, Math. Z. 265 (2010), no. 2, 481-491.
[61] T. Hmidi and S. Keraani, Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces, Adv. Math. 214 (2007), 618–638.
[62] D. Hoff and K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J. 44 (1995), no. 2, 603–676, DOI 10.1512/iumj.1995.44.2003. MR1355414
[63] H. Houamed, Well-posedness and long time behavior for the electron inertial Hallmagnetohydrodynamics system in Besov and Kato-Herz spaces, J. Math. Anal. Appl. 501 (2021), no. 2, chapter No. 125208, 23, DOI 10.1016/j.jmaa.2021.125208. MR4241621
[64] D. Iftimie, A uniqueness result for the Navier-Stokes equations with vanishing vertical viscosity, SIAM J. Math. Anal. 33 (2002), 1483–1493.
[65] K. Ishige and T. Kawakami, Refined asymptotic profiles for a semilinear heat equation, Math. Ann. 353 (2012), 161–192.
[66] T. Iwabuchi, Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior, Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), 687–713.
[67] T. Iwabuchi, A. Mahalov, and R. Takada, Stability of time periodic solutions for the rotating NavierStokes equations, Adv. Math. Fluid Mech., Birkhäuser/Springer, Basel, 2016, pp. 321–335.
[68] T. Iwabuchi and M. Nakamura, Small solutions for nonlinear heat equations, the Navier-Stokes equation and the Keller-Segel system in Besov and Triebel-Lizorkin spaces, Adv. Differential Equations 18 (2013), 687–736.
[69] T. Iwabuchi and T. Ogawa, Ill-posedness for the compressible Navier–Stokes equations under barotropic condition in limiting Besov spaces, J. Math. Soc. Japan 74 (2022), no. 2, 353–394.
[70] T. Iwabuchi and R. Takada, Time periodic solutions to the Navier-Stokes equations in the rotational framework, J. Evol. Equ. 12 (2012), no. 4, 985-1000.
[71] , Global solutions for the Navier-Stokes equations in the rotational framework, Math. Ann. 357 (2013), 727–741.
[72] , Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type, J. Funct. Anal. 267 (2014), no. 5, 1321-1337.
[73] , Dispersive effect of the Coriolis force and the local well-posedness for the Navier-Stokes equations in the rotational framework, Funkcial. Ekvac. 58 (2015), no. 3, 365-385.
[74] R. Ji, J. Wu, and W. Yang, Stability and optimal decay for the 3D Navier-Stokes equations with horizontal dissipation, J. Differential Equations 290 (2021), 57–77.
[75] H. Jia and R. Wan, Long time existence of classical solutions for the rotating Euler equations and related models in the optimal Sobolev space, Nonlinearity 33 (2020), 3763-3780.
[76] Y. Kagei and M. Okita, Asymptotic profiles for the compressible Navier-Stokes equations in the whole space, J. Math. Anal. Appl. 445 (2017), 297–317.
[77] M. Kato, Sharp asymptotics for a parabolic system of chemotaxis in one space dimension, Differential Integral Equations 22 (2009), 35–51.
[78] T. Kato, Nonstationary flows of viscous and ideal fluids in R3 , J. Functional Analysis 9 (1972), 296-305.
[79] T. Kato and C. Y. Lai, Nonlinear evolution equations and the Euler flow, J. Funct. Anal. 56 (1984), 15-28.
[80] T. Kato and G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41 (1988), 891-907.
[81] S. Kawashima, R. Nakasato, and T. Ogawa, Global wellposedness and time-decay estimate for the compressible Hall-magnetohydrodynamic system in the critical L 2 framework, preprint.
[82] M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), no. 5, 955–980.
[83] A. Kiselev and F. Nazarov, Global regularity for the critical dispersive dissipative surface quasigeostrophic equation, Nonlinearity 23 (2010), 549-554.
[84] A. Kiselev, F. Nazarov, and A. Volberg, Global well-posedness for the critical 2D dissipative quasigeostrophic equation, Invent. Math. 167 (2007), 445-453.
[85] Y. Koh, S. Lee, and R. Takada, Strichartz estimates for the Euler equations in the rotational framework, J. Differential Equations 256 (2014), 707-744.
[86] , Dispersive estimates for the Navier-Stokes equations in the rotational framework, Adv. Differential Equations 19 (2014), 857-878.
[87] P. Konieczny and T. Yoneda, On dispersive effect of the Coriolis force for the stationary NavierStokes equations, J. Differential Equations 250 (2011), no. 10, 3859-3873.
[88] H. Kozono, Y. Mashiko, and R. Takada, Existence of periodic solutions and their asymptotic stability to the Navier-Stokes equations with the Coriolis force, J. Evol. Equ. 14 (2014), no. 3, 565-601.
[89] H. Kozono and M. Nakao, Periodic solutions of the Navier-Stokes equations in unbounded domains, Tohoku Math. J. (2) 48 (1996), 33–50.
[90] H. Kozono, T. Ogawa, and Y. Taniuchi, Navier-Stokes equations in the Besov space near L∞ and BMO, Kyushu J. Math. 57 (2003), 303–324.
[91] L. Liu and T. Jin, Global Well-posedness for the Hall-magnetohydrodynamics system in larger critical Besov spaces, HAL Id: hal-02430536.
[92] S. Lee and R. Takada, Dispersive estimates for the stably stratified Boussinesq equations, Indiana Univ. Math. J. 66 (2017), no. 6, 2037–2070.
[93] J. Li and X. Zheng, The well-posedness of the incompressible magnetohydro dynamic equations in the framework of Fourier-Herz space, J. Differential Equations 263 (2017), 3419-3459.
[94] Y. Liu, M. Paicu, and P. Zhang, Global well-posedness of 3-D anisotropic Navier-Stokes system with small unidirectional derivative, Arch. Ration. Mech. Anal. 238 (2020), 805–843.
[95] Q. Liu and J. Zhao, Global well-posedness for the generalized magneto-hydrodynamic equations in the critical Fourier-Herz spaces, J. Math. Anal. Appl. 420 (2014), 1301-1315.
[96] T. Matsui, R. Nakasato, and T. Ogawa, Singular limit for the magnetohydrodynamics of the damped wave type in the critical Fourier-Sobolev space, J. Differential Equations 271 (2021), 414-446.
[97] C. Miao and B. Yuan, On the well-posedness of the Cauchy problem for an magnetohydrodynamics system in Besov spaces, Math. Methods Appl. Sci. 32 (2009), 53-76.
[98] H. Miura, Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space, Comm. Math. Phys. 267 (2006).
[99] T. Nagai, R. Syukuinn, and M. Umesako, Decay properties and asymptotic profiles of bounded solutions to a parabolic system of chemotaxis in Rn, Funkcial. Ekvac. 46 (2003), 383–407.
[100] T. Nagai and T. Yamada, Large time behavior of bounded solutions to a parabolic system of chemotaxis in the whole space, J. Math. Anal. Appl. 336 (2007), 704–726.
[101] R. Nakasato, Global well-posedness for the incompressible Hall-magnetohydrodynamic system in critical Fourier-Besov spaces, to appear in Journal of Evolution Equations.
[102] V.-S. Ngo and S. Scrobogna, Dispersive effects of weakly compressible and fast rotating inviscid fluids, Discrete Contin. Dyn. Syst. 38 (2018), no. 2, 749-789.
[103] H. Ohyama and R. Takada, Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer, J. Evol. Equ. 21 (2021), 2591–2629.
[104] M. Paicu, Équation anisotrope de Navier-Stokes dans des espaces critiques, Rev. Mat. Iberoamericana 21 (2005), 179–235 (French, with English summary).
[105] M. Paicu and P. Zhang, Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces, Comm. Math. Phys. 307 (2011), 713–759.
[106] J. Pedlosky, Geophysical Fluid Dynamics, Springer-Verlag New York, 1987.
[107] E. M. Stein and R. Shakarchi, Functional analysis, Princeton Lectures in Analysis, Princeton University Press, Princeton, NJ, 2011.
[108] J. Sun, M. Yang, and S. Cui, Existence and analyticity of mild solutions for the 3D rotating NavierStokes equations, Ann. Mat. Pura Appl. (4) 196 (2017), no. 4, 1203-1229.
[109] W. Shi and J. Xu, Global well-posedness for the compressible magnetohydrodynamic system in the critical L p framework, Math. Methods Appl. Sci. 42 (2019), 3662-3686.
[110] R. S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-714.
[111] R. Takada, Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type, J. Evol. Equ. 8 (2008), 693-725.
[112] , Long time existence of classical solutions for the 3D incompressible rotating Euler equations, J. Math. Soc. Japan 68 (2016), 579-608.
[113] , Long time solutions for the 2D inviscid Boussinesq equations with strong stratification, Manuscripta Math. 164 (2021), 223–250.
[114] R. Wan and J. Chen, Global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations, Z. Angew. Math. Phys. 67 (2016), Art. 104, 22.
[115] , Global well-posedness of smooth solution to the supercritical SQG equation with large dispersive forcing and small viscosity, Nonlinear Anal. 164 (2017), 54-66.
[116] R. Wan and Y. Zhou, On global existence, energy decay and blow-up criteria for the Hallmagnetohydrodynamics system, J. Differential Equations 259 (2015), 5982–6008.
[117] , Global well-posedness for the 3D incompressible Hall-magnetohydrodynamic equations with Fujita-Kato type initial data, J. Math. Fluid Mech. 21 (2019), chapter No. 5, 16.
[118] H. Wang and Z. Zhang, A frequency localized maximum principle applied to the 2D quasi-geostrophic equation, Comm. Math. Phys. 301 (2011), 105–129.
[119] J. Wu, Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces, SIAM J. Math. Anal. 36 (2004/05), 1014–1030.
[120] , Lower bounds for an integral involving fractional Laplacians and the generalized NavierStokes equations in Besov spaces, Comm. Math. Phys. 263 (2006), 803–831.
[121] L. Xu and P. Zhang, Enhanced dissipation for the third component of 3D anisotropic Navier-Stokes equations, arXiv:2107.06453.
[122] K. Yan and Z. Yin, Global well-posedness of the three dimensional incompressible anisotropic NavierStokes system, Nonlinear Anal. Real World Appl. 32 (2016), 52–73.
[123] T. Zhang, Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations in an anisotropic space, Comm. Math. Phys. 287 (2009), 211–224.
[124] T. Zhang and D. Fang, Global wellposed problem for the 3-D incompressible anisotropic NavierStokes equations, J. Math. Pures Appl. (9) 90 (2008), 413–449 (English, with English and French summaries).
[125] Z.-f. Zhang, Global well–posedness for the 2D critical dissipative quasi-geostrophic equation, Sci. China Ser. A 50 (2007), 485–494.
[126] H. Zhao and Y. Wang, A remark on the Navier-Stokes equations with the Coriolis force, Math. Methods Appl. Sci. 40 (2017), no. 18, 7323-7332.