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arXiv · 2211.00836

Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations

Wenhui Chen·Ryo Ikehata
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Abstract

In this paper, we consider the linearized compressible Navier-Stokes equations in the whole space $\mathbb{R}^n$. Concerning initial datum with suitable regularities, we introduce a new threshold $|\mathbb{B}_0|=0$ to distinguish different large-time behaviors. Particularly in the lower-dimensions, optimal growth estimates ($n=1$ polynomial growth, $n=2$ logarithmic growth) hold when $|\mathbb{B}_0|>0$, whereas optimal decay estimates hold when $|\mathbb{B}_0|=0$. Furthermore, we derive asymptotic profiles of solutions with weighted $L^1$ datum as large-time.

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Wenhui Chen, Ryo Ikehata. 2022-11-02. Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations. https://doi.org/10.57262/die037-0910-699

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