学术报告(李明杰、姚磊、吕勇、王焰金、王超 9.20)

发布人:周妍 发布日期:2019-09-17
活动时间
-
活动地址
数学楼416讲学厅

主讲人   李明杰(中央民族大学)14:00-14:40

 

题目:Global strong solutions to the Cauchy problem for planar non-resistive magnetohydrodynamic equations with large initial data

摘要:In this talk, we consider the Cauchy problem to the  compressible planar magnetohydrodynamic equations without heat conduction nor magnetic diffusion, and establish the local and global existence and uniqueness of strong solutions with general large initial data. This is a joint work with Professor Jinkai Li.

 

 

主讲人   姚磊(西北大学)14:40-15:20

 

题目:Hydrodynamic limit for inhomogeneous incompressible Navier-Stokes/ Vlasov-Fokker-Planck equations

摘要:We study the hydrodynamic limit for inhomogeneous incompressible Navier-Stokes/ Vlasov-Fokker-Planck equations in a two-dimensional bounded domain. The proof relies on the relative entropy method and a compactness result $L_M\hookrightarrow\hookrightarrow H^{-1}$ of Orlicz spaces in 2D  to obtain the strong convergence of the macroscopic density of the particles. This result also holds for 3D case when the initial density of the fluid has positive lower bound, thus extends the works of Goudon-Jabin-Vasseur[Indiana Univ. Math. J., 53(2004)] and Mellt-Vasseur [Comm. Math. Phys., 281(2008)] from incompressible and compressible Navier-Stokes/Vlasov-Fokker-Planck equations to inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations. At last, we give a recent result about the hydrodynamic limit of 1D compressible Navier-Stokes-Vlasov equations.

 

 

主讲人   吕勇(南京大学)15:20-16:00

 

题目:Resonances and instabilities in geometric optics

摘要:It is used the name geometric optics for the study of highly oscillating solutions to hyperbolic systems. The main issue is the stability of a family of approximate solutions called WKB solutions in the short wavelength limit. The main obstacle to such a stability analysis is the resonance.  In this lecture, we will discuss systematically the relationship between resonances and stabilities. In particular, we will describe the mechanism how resonances may destabilize WKB solutions. Collaborators include Eric Dumas (Grenoble), Benjamin Texier (Paris), Zhifei Zhang (Beijing).

 

 

主讲人   王焰金(厦门大学)16:00-16:40

 

题目:On the construction of solutions to free boundary problems

摘要:In this talk we will present our local well-posedness of the free-surface incompressible Navier-Stokes equations and the incompressible ideal MHD. We will focus on the construction of approximate solutions.

 

 

主讲人   王超(北京大学)16:40-17:20

 

题目:Zero viscosity limit for the Naiver-Stokes equation in a thin domain

摘要:In this talk, we justify the formal limit of the Navier-Stokes system in a thin domain, under certain constraints on the aspect ratio and Reynolds munber. Like the classical boundary layer problem, this problem still lose one-derivative which implies the limit holds under the analytic norm. Here, we archiev it under the Gevrey class with the index 9/8.