arXiv subjects

Mengqian Liu

Publications and source records attributed to Mengqian Liu.

3 recordsLinked to original sources

arXiv2024

The global strong solution to compressible system with fractional viscous term

In this paper, we study the Cauchy problem to the 3D fractional compressible isentropic generalized Navier-Stokes equations for viscous compressible fluid with one Levy diffusion process. We obtain the existence and uniqueness of global strong solution for small initial data by providing several commutators via the Littlewood-Paley theory. Moreover, we derive $L^2$-decay rate for the highest derivative of the strong solution without decay loss by using a cancellation of a low-medium-frequency quantity. Our results improve the results provided in [J. Differential Equations 377(2023): 369-417].

math.AP↗

arXiv2024

Global strong solution to the inviscid liquid-gas two-phase flow model in $L^p$ framework

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.

math.AP↗

arXiv2023

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

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.

math.AP↗