arXiv subjects
Publications and source records attributed to Juanzi Cai.
This paper is dedicated to the study of the inviscid liquid-gas two-phase flow model in $\mathbb{R}^d\ (d\geq1)$. We establish the global existence of strong solutions to this system with small initial data in hybrid Besov spaces based on general $L^p$-norms. Additionally, we obtain the decay estimates of solutions rely on the constructed Lyapunov functional.
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.
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.