The limit problem of the Patlak-Keller-Segel-Stokes system in scalling
critical space
Abstract
In this paper, we consider a singular limit problem of Cauchy problem
for Patlak-Keller-Segel equation coupled with Stokes equation in
scalling critical space. Precisely, by taking advantage of a coupling
structure of equations and using a scale decomposition technique, it is
shown that when the relaxation time parameter ε →∞, a solution of
Patlak-Keller-Segel system coupled with nonstationary Stokes equation
converges to that of Patlak-Keller-Segel system coupled with stationary
Stokes equation in the critical Fourier-Besov space under certain
conditions.