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 HγN. More precisely, for any integer N≥3, we sh...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-07, Vol.535 (2), p.128186, Article 128186
Main Authors: Wu, Wanping, Zhang, Yinghui
Format: Article
Language:English
Subjects:
Micropolar fluids system
Space–time decay rates
Weighted estimate
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128186