Global well-posedness and large time behavior of the viscous liquid-gas two-phase flow model in $\mathbb R^3$

：张映辉教授
：2019-06-20 11:00
：数理大楼661

       Speaker：Prof. Yinghui Zhang

                        Guangxi Normal University

Title:  Global well-posedness large time behavior of the viscous liquid-gas two-phase flow model in $\mathbb R^3$

       Time：20  June 2019, 11:00

Location：数理大楼661

Abstract:  We investigate the Cauchy problem of the viscous liquid-gas two-phase flow model in $\mathbb R^3$. Under the assumption that the initial data is close to the constant equilibrium state in the framework of Sobolev space $H^2(\mathbbR^3)$, the Cauchy problem is shown to be globally well-posed by an ingenious energy method. If additionally, for $1\leq p<\frac{6}{5}$, $L^p$-norm of the initial perturbation is bounded, the optimal convergence rates of the solutions in $L^q$-norm with $2\leq q\leq 6$ optimal convergence rates of their spatial derivatives in $L^2$-norm are also obtained by combining spectral analysis with energy methods.

Speaker  Introduction：张映辉，博士，教授，硕士生导师，广西师范大学B类漓江学者，美国《数学评论》评论员，现任数学与统计学院院长助理。主持国家自然科学基金项目2项，省部级科研项目8项；主要研究方向为流体力学中的偏微分方程；已在Indiana Univ. Math. J.、J. Differ. Equations.、P. Roy. Soc. Edinb. A、J. Math. Phys.、中国科学（英文版）等国内外权威期刊发表论文近40篇，SCI收录30篇；获湖南省自然科学奖和市科技进步奖各1项。

 

        联系人：王焰金教授