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arXiv · 2103.04298

Bounded weak and strong time periodic solutions to a three-dimensional chemotaxis-Stokes model with porous medium diffusion

Hailong Ye·Chunhua Jin
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Abstract

In this paper, we study the time periodic problem to a three-dimensional chemotaxis-Stokes model with porous medium diffusion $\Delta n^m$ and inhomogeneous mixed boundary conditions. By using a double-level approximation method and some iterative techniques, we obtain the existence and time-space uniform boundedness of weak time periodic solutions for any $m>1$. Moreover, we improve the regularity for $m\le\frac{4}{3}$ and show that the obtained periodic solutions are in fact strong periodic solutions.

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Hailong Ye, Chunhua Jin. 2021-03-07. Bounded weak and strong time periodic solutions to a three-dimensional chemotaxis-Stokes model with porous medium diffusion. https://doi.org/10.1063/5.0049141

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