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

Authors：Zeng, Lan; Zhang, Zhifei; Zi, Ruizhao^*

Source：Journal of Functional Analysis, 2021, 280(10): 108967.

DOI：10.1016/j.jfa.2021.108967

• Patlak-Keller-Segel equation
• Navier-Stokes equation
• Couette flow
• Enhanced dissipation

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.

• Institution
  北京大学