报告题目：Nonlinearly exponential stability for the compressible Navier-Stokes equations with temperature-dependent transport coefficients

报告人：张剑文（厦门大学）

报告时间：2021年7月7日上午9：00-11：00

报告地点：数学与计算机科学学院4号楼302室

报告摘要：This paper is concerned with an initial and boundary value problem of the compressible Navier-Stokes equations for one-dimensional viscous and heat-conducting ideal polytropic fluids with temperature-dependent transport coefficients. In the case when the viscosity μ(θ)=θα and the heat-conductivity κ(θ)=θβ with α,β∈[0,∞), we prove the global-in-time existence of strong solutions under some assumptions on the growth exponent α and the initial data. As a byproduct, the nonlinearly exponential stability of the solution is obtained. It is worth pointing out that the initial data could be large if α≥0 is small, and the growth exponent β≥0 can be arbitrarily large.

个人简介：张剑文，男，厦门大学数学科学学院教授、博导、副院长。主要研究方向为流体力学中的非线性偏微分方程（组），在Navier-Stokes、MHD、Boussinesq方程的适定性、正则性、稳定性、长时间性质和小参数极限等问题中取得许多进展性研究成果，并发表在SIMA、IUMJ、M3AS、JDE、JNLS、Nonlinearity等期刊上近50篇。连续主持多项国家自然科学基金项目，曾作为主要参与人获福建省自然科学奖二等奖、国家教学成果奖二等奖、福建省教学成果特等奖。