Global existence and boundedness of weak solutions to a chemotaxis-Stokes system with rotational flux term

摘要

In this paper, the three-dimensional chemotaxis-Stokes system posed in a bounded domain subset of>R3 with smooth boundary is considered under the no-flux boundary condition for n, c and the Dirichlect boundary condition for u under the assumption that the Frobenius norm of the tensor-valued chemotactic sensitivity S(x,n,c) satisfies S(x,n,c)2 for some non-decreasing function SC2. In the present work, it is shown that the weak solution is global in time and bounded while m > m* (l), where l > 2 31/12.