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Well-posedness of mild solutions to the drift-diffusion and the vorticity equations in amalgam spaces

Suguro, Takeshi 京都大学 DOI:10.1016/j.jmaa.2022.126843

2023.04.01

概要

We consider the Cauchy problem of the drift-diffusion and the vorticity equations. Both equations involve the Poisson equation and a nonlocal effect of the Green's function influences the solution to the problem. In this paper, we study the well-posedness of the drift-diffusion and the vorticity equations by using amalgam spaces of Lebesgue spaces. Moreover, we show the unconditional uniqueness of mild solutions to the drift-diffusion equation in amalgam spaces.

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