Space–time decay rates for the 3D compressible micropolar fluids system

Abstract

We investigate space–time decay rates of solutions to the 3D Cauchy problem of the compressible micropolar fluids system, and the main novelty of this work is two–fold: First, we establish the space–time decay rate of solution in weighted Sobolev space HγN. More precisely, for any integer N≥3, we show that the space–time decay rate of the k(∈[0,N])–order spatial derivative of the solution in weighted Lebesgue space Lγ2 is (1+t)−34−k2+γ. Second, we prove that the space–time decay rate of k(∈[0,N−1])–order spatial derivative of the micro–rotational velocity in weighted Lebesgue space Lγ2 is (1+t)−54−k2+γ, which is faster than ones of the density and the velocity.