Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded weak and strong time periodic solutions to a three-dimensional
  chemotaxis-Stokes model with porous medium diffusion   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.

13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph