数学研究所

数学科学全国重点实验室

调和分析及其应用研究中心

学术报告

偏微分方程研讨班

Speaker: 张荣（南昌大学）

Inviter: 黄祥娣 研究员

Language: Chinese

Title: Global existence and large-time behavior of solutions to one-dimensional compressible Navier–Stokes system with outer pressure in the half-space

Time&Venue: 2025年6月3日（星期二）9:00-10:00

& 南楼N820

Abstract: We consider the outer pressure problem of the compressible Navier–Stokes system in the Lagrangian coordinate system describing the one-dimensional motion of a viscous heat-conducting prefect polytropic gas in half-space. Both the specific volume and the temperature are proved to be bounded from below and above independently of both space and time, and as a direct consequence, the global existence and large-time behavior of strong solutions for the outer pressure problem in the half-space is also obtained. This is a joint work with X Han and Y Wu.

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Title:Global strong solutions to the incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum in 3D exterior domains

Time&Venue: 2025年6月4日（星期三）9:00-10:00

& 南楼N820

Abstract:We consider the nonhomogeneous incompressible MHD Equations with density-dependent viscosity in 3D exterior domains with slip boundary conditions. The key is the constraint of an additional initial value condition B_0∈ L^p (1⩽ p< 12/7), which increase decay-in-time rates of the solutions, thus we obtain the global existence and uniqueness of strong solutions provided the gradient of the initial velocity and initial magnetic field is suitably small. In particular, the initial density is allowed to contain vacuum states and large oscillations. This is a joint work with B Yuan and P Zhou.

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Title:Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosity

Time&Venue: 2025年6月6日（星期五）9:00-10:00

& 南楼N820

Abstract: We study the compressible QNS equations with degenerate viscosity in the 3D periodic domains. For QNS with or without additional damping terms, motivated by the recent works of Li and Xin [e-print arXiv: 1504.06826] and P. Antonelli and S. Spirito [Arch. Ration. Mech. Anal. 225, 1161–1199 (2017)], we construct a suitable approximate system which has smooth solutions satisfying the energy inequality and the BD entropy estimate, we obtain the global existence of weak solutions to the compressible QNS equations with or without damping terms for large initial data. This is a joint work with B Lv and X Zhong.