Optimal time decay of the compressible micropolar fluids

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Liu, Qingqing¹  Zhang, Peixin² 

[1] S China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

[2] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Peoples R China

关键词: Compressible micropolar fluids;    Global smooth solution;    Optimal time decay;   

DOI  :  10.1016/j.jde.2016.01.037

来源: Elsevier

【 摘 要 】

This paper primarily studies the large-time behavior of solutions to the Cauchy problem on the compressible micropolar fluid system which is a generalization of the classical Navier-Stokes system. The asymptotic stability of the steady state with the strictly positive constant density, the vanishing velocity, and micro-rotational velocity is established under small perturbation in regular Sobolev space. Moreover, it turns out that both the density and the velocity tend time-asymptotically to the corresponding equilibrium state with rate (1 +t)(-3/4) in L-2 and the micro-rotational velocity also tends to the equilibrium state with the faster rate (1 +t)(-5/4) in L-2 norm. The proof is based on the spectrum analysis and time-weighted energy estimate. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free