Keller-Segel-Stokes interaction involving signal-dependent motilities

The chemotaxis-Stokes system [GRAPHICS] is considered along with homogeneous boundary conditions of no-flux type for n and c, and of Dirichlet type for u, in a smoothly bounded domain Omega subset of R-2. Under the assumption that Phi is an element of W-2,W-infinity(Omega), that phi is an element of C-0((0, infinity)) is bounded on each of the intervals (xi(0), 8) with arbitrary xi(0) > 0, and that with some k(phi) > 0 and alpha > 0, we have [GRAPHICS] It is shown that for any suitably regular initial data, an associated initial-boundary value problem admits a global very weak solution.

Automated summary

This article investigates the chemotaxis-Stokes system with homogeneous boundary conditions of no-flux type for n and c, and of Dirichlet type for u, in a smoothly bounded domain Omega subset of R-2. It is shown that under the given assumptions, a global very weak solution exists for any suitably regular initial data in the associated initial-boundary value problem.