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

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 H1,'. More precisely, for any integer N >= 3, we show that the space-time decay rate of the k (is an element of [0, N])-order spatial derivative of the solution in weighted Lebesgue space L21, is (1 + t)-34- 2 k+1,. Second, we prove that the space-time decay rate of k (is an element of [0, N - 1])-order spatial derivative of the micro-rotational velocity in weighted Lebesgue space L21, is (1 + t)-54 - 2k+1,, which is faster than ones of the density and the velocity. (c) 2024 Elsevier Inc. All rights reserved.