报告时间

2021年11月27日下午3点-5点

报告地点

腾讯会议ID：680 487 831

主办单位

数学与统计学院

报告题目

Global regular solutions for 1D degenerate compressible Navier-Stokes equations with large data and far field vacuum

报告范围

数学与统计学院青年教师、研究生及高年级本科生

报告人学术简历

朱圣国，男，上海交通大学数学科学学院特聘研究员。2015年于上海交通大学获理学博士学位。曾先后在香港中文大学数学科学研究所、澳大利亚莫纳什大学数学学院、英国牛津大学数学研究所做博士后。主要从事与流体力学及相对论相关的非线性偏微分方程的理论研究工作，在可压缩Navier-Stokes及Euler方程组的适定性和奇异性方面取得了一系列重要进展。目前已在国际学术期刊上发表学术论文20余篇，其中包括Advances in Mathematics、Arch. Ration. Mech. Anal.、Ann. Inst. H. Poincare Anal. Non Lineaire、J. Math. Pures Appl.等本领域权威杂志。 并于2017年入选英国皇家学会”Newton International Fellow”。

报告内容

框架

For compressible isentropic Navier-Stokes equations, whenthe viscosity coefficient depends on the density in a sublinear power law, based on an elaborate analysis of the intrinsic singular structure of this degenerate system, we prove the global-in-time well-posedness of regular solutions with conserved total mass, momentum, and finite total energy in some inhomogeneous Sobolev spaces. The key to the proof is the introduction of a well-designed reformulated structure by introducing some new variables and initial compatibility conditions, which, actually, can transfer the degeneracies of the time evolution and the viscosity to the possible singularity of some special source terms. Then, combined with the BD entropy estimates and transport properties of the so-called effective velocity, one can obtain the required uniform a priori estimates of corresponding solutions. This talk is based on a joint work with Yue Cao (SJTU) and Hao Li (Fudan).