[1] M. Ben-Artzi, Global solutions of two-dimensional Navier-Stokes and Euler equations, Arch. Ration. Mech. Anal. 128 (1994) 329–358.
[2] J.-P. Bertrandias, C. Datry, C. Dupuis, Unions et intersections d’espaces Lp invariantes par translation ou convolution, Ann. Inst. Fourier (Grenoble) 28 (1978) v, 53–84.
[3] P. Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation, Stud. Math. 114 (1995) 181–205.
[4] P. Biler, M. Cannone, I.A. Guerra, G. Karch, Global regular and singular solutions for a model of gravitating particles, Math. Ann. 330 (2004) 693–708.
[5] Z. Bradshaw, C.-C. Lai, T.-P. Tsai, Mild solutions and spacetime integral bounds for Stokes and Navier-Stokes flows in Wiener amalgam spaces, arXiv:2207.04298.
[6] Z. Bradshaw, T.-P. Tsai, Local energy solutions to the Navier-Stokes equations in Wiener amalgam spaces, SIAM J. Math. Anal. 53 (2021) 1993–2026.
[7] H. Brezis, T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math. 68 (1996) 277–304.
[8] R.C. Busby, H.A. Smith, Product-convolution operators and mixed-norm spaces, Trans. Am. Math. Soc. 263 (1981) 309–341.
[9] T. Cazenave, F.B. Weissler, Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z. 228 (1998) 83–120.
[10] L. Corrias, B. Perthame, H. Zaag, Global solutions of some chemotaxis and angiogenesis systems in high space dimensions, Milan J. Math. 72 (2004) 1–28.
[11] S. Cygan, G. Karch, K. Krawczyk, H. Wakui, Stability of constant steady states of a chemotaxis model, J. Evol. Equ. 21 (2021) 4873–4896.
[12] H.G. Feichtinger, Generalized amalgams, with applications to Fourier transform, Can. J. Math. 42 (1990) 395–409.
[13] J.J.F. Fournier, J. Stewart, Amalgams of Lp and lq, Bull. Am. Math. Soc. (N.S.) 13 (1985) 1–21.
[14] H. Fujita, T. Kato, On the Navier-Stokes initial value problem. I, Arch. Ration. Mech. Anal. 16 (1964) 269–315.
[15] Y. Giga, T. Miyakawa, Navier-Stokes flow in R3 with measures as initial vorticity and Morrey spaces, Commun. Partial Differ. Equ. 14 (1989) 577–618.
[16] Y. Giga, T. Miyakawa, H. Osada, Two-dimensional Navier-Stokes flow with measures as initial vorticity, Arch. Ration. Mech. Anal. 104 (1988) 223–250.
[17] K. Gröchenig, C. Heil, K. Okoudjou, Gabor analysis in weighted amalgam spaces, Sampl. Theory Signal Image Process. 1 (2002) 225–259.
[18] F. Holland, Harmonic analysis on amalgams of Lp and lq, J. Lond. Math. Soc. (2) 10 (1975) 295–305.
[19] T. Iwabuchi, Global well-posedness for Keller-Segel system in Besov type spaces, J. Math. Anal. Appl. 379 (2011) 930–948.
[20] T. Iwabuchi, M. Nakamura, Small solutions for nonlinear heat equations, the Navier-Stokes equation, and the Keller-Segel system in Besov and Triebel-Lizorkin spaces, Adv. Differ. Equ. 18 (2013) 687–736.
[21] T. Iwabuchi, T. Ogawa, Ill-posedness issue for the drift diffusion system in the homogeneous Besov spaces, Osaka J. Math. 53 (2016) 919–939.
[22] W. Jäger, S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Am. Math. Soc. 329 (1992) 819–824.
[23] T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Ration. Mech. Anal. 58 (1975) 181–205.
[24] T. Kato, Strong Lp-solutions of the Navier-Stokes equation in Rm , with applications to weak solutions, Math. Z. 187 (1984) 471–480.
[25] E.F. Keller, L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970) 399–415.
[26] N. Kikuchi, E. Nakai, N. Tomita, K. Yabuta, T. Yoneda, Calderón-Zygmund operators on amalgam spaces and in the discrete case, J. Math. Anal. Appl. 335 (2007) 198–212.
[27] H. Koch, D. Tataru, Well-posedness for the Navier-Stokes equations, Adv. Math. 157 (2001) 22–35.
[28] H. Kozono, Y. Sugiyama, Local existence and finite time blow-up of solutions in the 2-d Keller-Segel system, J. Evol. Equ. 8 (2008) 353–378.
[29] H. Kozono, Y. Sugiyama, Y. Yahagi, Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller- Segel system, J. Differ. Equ. 253 (2012) 2295–2313.
[30] M. Kurokiba, T. Ogawa, Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type, Differ. Integral Equ. 16 (2003) 427–452.
[31] M. Kurokiba, T. Ogawa, Well-posedness for the drift-diffusion system in Lp arising from the semiconductor device simu- lation, J. Math. Anal. Appl. 342 (2008) 1052–1067.
[32] P.G. Lemarié-Rieusset, Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller- Segel equations in the whole space, Adv. Differ. Equ. 18 (2013) 1189–1208.
[33] Y. Maekawa, Y. Terasawa, The Navier-Stokes equations with initial data in uniformly local Lp spaces, Differ. Integral Equ. 19 (2006) 369–400.
[34] T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci. Appl. 5 (1995) 581–601.
[35] T. Nagai, M. Mimura, Asymptotic behavior for a nonlinear degenerate diffusion equation in population dynamics, SIAM J. Appl. Math. 43 (1983) 449–464.
[36] T. Ogawa, S. Shimizu, The drift-diffusion system in two-dimensional critical Hardy space, J. Funct. Anal. 255 (2008) 1107–1138.
[37] C.S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys. 15 (1953) 311–338.
[38] T. Suguro, Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces, J. Evol. Equ. 21 (2021) 4599–4618.
[39] N. Wiener, On the representation of functions by trigonometrical integrals, Math. Z. 24 (1926) 575–616.
[40] N. Wiener, Tauberian theorems, Ann. Math. (2) 33 (1932) 1–100.