[09-21] 2022年秋季偏微分方程学术报告会
报告题目：Stability of planar rarefaction wave for a 2D hyperbolic-elliptic coupled system on half space
报告人：朱长江 华南理工大学数学学院
报告摘要:In this talk, we will introduce the asymptotic stability of solution to an initial-boundary value problem for a hyperbolic-elliptic coupling system on two-dimensional half space. We show that the solution to the problem converges to the corresponding planar rarefaction wave as time tends to infinity. To our knowledge, the stability result of planar rarefaction wave on half space focus primarily on the single viscosity conservation law because the rarefaction wave (one-dimensional diffusion wave) of the corresponding one-dimensional problem to scalar viscosity conservation law is known. In other words, for a general high dimensional system of equations, we cannot obtain the stability of planar rarefaction wave on half space because we cannot construct the rarefaction wave of the corresponding one-dimensional problem. In this paper, we use the structure of the hyperbolic-elliptic coupling system to obtain the monotonic rarefaction wave of the corresponding one-dimensional problem, and hence give the stability of the plane rarefaction wave on half space.This is a joint work with Minyi Zhang.
报告人简介：朱长江，博士，华南理工大学教授、博士生导师，享受国务院政府特殊津贴，国家杰出青年基金获得者，国际数学学术期刊《Kinetic and Related Models》、《ActaMathematica Scientia》中英文版等杂志编委，《数学教育学报》副主编，教育部高等学校数学类教学指导委员会委员，教育部“创新团队发展计划”、国家自然科学基金重点项目、国家级教学团队、国家级一流本科专业、国家级精品课程、精品资源共享课程和一流本科课程负责人，全国百篇优秀博士学位论文指导教师。主持完成的研究成果获教育部自然科学奖二等奖，教学成果两次获国家级教学成果奖二等奖。2012年被评为全国优秀科技工作者，2017年入选国家“万人计划”教学名师，2020年获中国教师发展基金会杰出教学奖，2021年获华南理工大学教学终身成就奖。
报告题目: Global existence in critical spaces for non Newtonian compressible viscoelastic flows
报告人：徐江 南京航空航天大学数学学院
报告摘要：We are concerned with the multi-dimensional compressible viscoelastic flows of Oldroyd type. In order to capture the damping effect of the additional deformation tensor, to the best of our knowledge, the “div-curl”conditions play a key role in previous efforts. Our aim is to remove the structural conditions and establish a global existence of strong solutions to compressible viscoelastic flows in critical spaces. In absenceof compatible conditions, the new effective flux is introduced, which enables us to capture the dissipation arising from combination of density and deformation tensor. It was shown that the partial dissipation in non-Newtonian compressible fluids was weaker than that of classical Navier-Stokes equations.
报告人简介：徐江南京航空航天大学数学学院教授（青年破格）、博士生导师、副院长。2007年在浙江大学获博士学位。主要研究一类耗散型偏微分方程的数学理论，成果出版在《Comm.Math.Phys.》、《Arch.Rational Mech.Anal.》等国际期刊上。主持四项国家自然科学基金项目和参加一项国家自然科学基金重点项目。日本九州大学的访问教授和早稻田大学的公派高级研究学者。2014年入选教育部“新世纪优秀人才支持计划”，2019年入选教育部“长江学者奖励计划”青年学者。
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