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arXiv · 2312.09447

Compressible Navier-Stokes equations without heat conduction in Lp-framework

Juanzi Cai·Zhigang Wu·Mengqian Liu
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Abstract

In this paper, we mainly consider global well-posedness and long time behavior of compressible Navier-Stokes equations without heat conduction in $L^p$-framework. This is a generalization of Peng and Zhai \cite{peng}(SIMA, 55(2023), no.2, 1439-1463), where they obtained the corresponding result in $L^2$-framework. Based on the key observation that we can release the regularity of non-dissipative entropy $S$ in high frequency in \cite{peng}, we ultimately achieve the desired $L^p$ estimate in the high frequency via complicated calculations on the nonlinear terms. In addition, we get the $L^p$-decay rate of the solution.

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Juanzi Cai, Zhigang Wu, Mengqian Liu. 2023-12-15. Compressible Navier-Stokes equations without heat conduction in Lp-framework. https://arxiv.org/abs/2312.09447

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