Stability and instability for compressible Navier-Stokes equations with Yukawa potential

Juanzi Cai; Zhiang Wu; Guochun Wu

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arXiv · 2308.16387

Stability and instability for compressible Navier-Stokes equations with Yukawa potential

Juanzi Cai·Zhiang Wu·Guochun Wu

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Abstract

In this paper, we first consider global well-posedness and long time behavior of compressible Navier-Stokes equations with Yukawa-type potential in $L^p$-framework under the stability condition $P'(\barρ)+γ\barρ>0$. Here $\barρ>0$ is the background density, P is the pressure and $γ\in\mathbb{R}$ is Yukawa coefficient. This is a continuity work of Chikami \cite{chikami1} concerning on local existence and blow-up criterion. On the other hand, we study the instability of the linear and nonlinear problem of the system when $P'(\barρ)+γ\barρ<0$ in the Hadamard sense.

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Juanzi Cai, Zhiang Wu, Guochun Wu. 2023-08-31. Stability and instability for compressible Navier-Stokes equations with Yukawa potential. https://arxiv.org/abs/2308.16387

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