| Contents |
| We'd like to consider the existence of solutions $(n,c,u,P)$ to Keller-Segel-Stokes systems (KSS), where components of the solution denote the bacteria density, the chemical concentration, the velocity field of the fluid and the pressure in the order of inputting. The analysis of this system is very difficult, but there are few results upon the global-in-time existence: As to the 2D case, there are results on the global existence in (KSS) with the linear diffusion ($\Delta n$) on $\mathbb{R}^2$ and with quasilinear degenerate diffusion ($\Delta n^m$, $m>1$) on bounded convex domains. Moreover in the 3D case, we know the global existence in (KSS) with $\Delta n^\frac{4}{3}$ on $\mathbb{R}^3$ and with $\Delta n^m$ ($m>\frac{8}{7}$) on bounded convex domains. As can be seen from these, there are many open interesting problems. In this talk we'd like to discuss these problems. |
|