Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Couette flow

摘要

In this paper, we consider the two dimensional Patlak-Keller-Segel-Navier-Stokes system near the Couette flow (Ay, 0) in T x R. It is shown that if A is large enough, the solution to the system stays globally regular. Both the parabolic-parabolic case and the parabolic-elliptic case are investigated. In particular, for the parabolic-parabolic case, an extra smallness assumption on the initial chemical gradient parallel to(del c(in))not equal parallel to(L2) is needed to control the mixing destabilizing effect. (C) 2021 Elsevier Inc. All rights reserved.