Abstract: 

In this paper, we consider the large time behavior of the weak solution to the free boundary problem for one-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosity and vacuum. Under appropriate smallness conditions on the initial data (initial energy), we give the optimal decay rate of the density function along with the behavior of it near the vacuum interfaces is studied. In the meanwhile, we obtain also sharper decay rates for the norms in terms of the velocity function. The key is to establish some new global-in-time weighted estimates (both in time and space) uniformly up to the vacuum boundary.

This is a joint work with Guangyi Hong.

个人简介：

朱长江，博士，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》、《ISRN Mathematical Analysis》、《Acta Mathematica Scientia》、《数学物理学报》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、国家级精品课程和国家精品资源共享课程负责人，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。