Asymptotic stability of planar rarefaction wave to 3D micropolar equations

Abstract

We are concerned with the large-time behavior of the Cauchy problem to the 3d micropolar fluids in an infinite long flat nozzle domain R×T2. In one dimensional case, this system tends time-asymptotically to the Navier–Stokes equations. That is to say, the basic wave patterns to the compressible micropolar fluids model are stable. Hence, in this paper we consider the nonlinear stability of planar rarefaction wave to the corresponding three dimensional model. Some cancellations on the flux terms and viscous terms are crucial. Moreover, a proper combining of damping term and rotation terms can provide an extra regularity of w.