Optimal time decay of the compressible micropolar fluids with discontinuous initial data in 3D

Abstract

The global existence of weak solutions to Cauchy problem for compressible micropolar fluids with discontinuous initial data has been established in [4]. However, the optimal decay rates of these weak solutions remain an open problem. The current work is to show the optimal decay rates of these weak solutions in Lr-norm with 2<r≤∞ and the optimal decay rates of the first order derivative of the velocity and micro-rotational velocity in L2-norm which are the same as the rates of classical solutions in [20]. In this process, we combine electromagnetic and fluid decomposition, frequency domain decomposition, and construct a series of temporal energy functional to solve complex nonlinear problems with low regularity.