活动时间：2022-10-12 10:00

活动地点：腾讯会议 110-884-176

主讲人：张鑫

主讲人中文简介：

张鑫老师现任同济大学数学科学学院助理教授, 其本科毕业于山东大学数学学院，博士毕业于巴黎第十二大学( Université Paris-Est Créteil Val-de-Marne), 导师是 Danchin Raphaël 教授, 并在早稻田大学从事博士后研究, 合作导师是 Shibata Yoshihiro 教授。其研究方向为流体力学方程的偏微分方程分析理论, 相关研究结果已发表于 Comm. Partial Differential Equations、  J. Éc. polytech. Math、 SIAM J. Math. Anal. 等知名数学杂志。

活动内容摘要：

In this talk, we discuss about the problem concerning the motion of the barotropic compressible Navier-Stokes equations (CNS) in the smooth exterior domain with some free surface. By applying the method of (full or partial) Lagrangian coordinates, the nonlinear problem reduces to the study of the Lame system with the free boundary conditions. Then the $L_p$-$L_q$ decay estimates are established for such linearized system, by taking advantage of the local energy approach. At last, we apply the $L_p$-$L_q$ decay theory to construct the global solution of (CNS). In particular, we have established the classical Matsumura-Nishida theory for the free boundary value problem via the partial Lagrangian approach. All the results above are based on the joint works with Prof. Yoshihiro Shibata from Waseda University.

主持人：查冬兵