Workshop on Singular Limit and Related Problems

Renmin University of China, Beijing, China

June 3, 2018

Title and Abstract

Three-Scale Singular Limits of Evolutionary PDEs

Steve Schochet

Tel Aviv University

E-mail address: Schochet@post.tau.ac.il

Abstract: Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly bounded for a fixed time as the two parameters tend to zero at different rates. A simple example shows the necessity of those conditions in order for uniform bounds to hold. Under further conditions the solutions of the original system tend to solutions of a limit equation as the parameters tend to zero. Joint work with Bin Cheng and Qiangchang Ju.

Boltzmann equation with initial large amplitude data

Feimin Huang (黄飞敏)

Chinese Academy of Sciences

E-mail address: fhuang@amt.ac.cn

 

Incompressible limit of the degenerate quantum compressible Navier-Stokes equations

Fucai Li (栗付才)

Nanjing University

E-mail address: fli@nju.edu.cn

Abstract: In this talk we shall discuss the incompressible limit to the degenerate quantum compressible Navier-Stokes equations in a periodic domain and the whole space with general initial data.

Behaviors of Navier-Stokes(Euler)-Fokker-Planck equations

Hailiang Li (李海梁)

Capital Normal University

E-mail address: hailiang_li@mail.cnu.edu.cn

Abstract: We consider the behaviors of global solutions to the initial value problems for the multi-dimensional compressible Navier-Stokes(Euler)-Fokker-Planck equations. It is shown that due the micro-macro coupling effects, the sound wave type propagation of this NSFP or EFP system for two-phase fluids is observed with the wave speed determined by the two-phase fluids. This phenomena can no be obsered for the pure Fokker-Planck equation.

Small Alfven number limit of the compressible magnetohydrodynamic equations

Qiangchang Ju (琚强昌)

Institute of Applied Physics and Computational Mathematics

E-mail address: ju_qiangchang@iapcm.ac.cn

Abstract：Even though much progress has been made in proving the singular limits of quasi-linear hyperbolic system with small parameters since the classical work by Klainerman and Majda , there are no rigorous proofs for small Alfv\'{e}n number limit of the compressible magnetohydrodynamic flows except the work by Browning and Kreiss under unnatural initial conditions. In this talk, some recent studies on small Alfven number limit of the compressible magnetohydrodynamic equations will be presented under appropriate conditions.

Quasineutral Limit of Drift-diffusion Models for Semiconductors and the Related Models

Shu Wang (王术)

Beijing University of Technology

E-mail address: wangshu@bjut.edu.cn

Abstract: In this talk I will discuss quasineutral limit of Drift-diffusion models for semiconductors and the related models. Quasineutrality assumption is one basic physical assumption,raised by W. Van Roosbroeck (Bell System Tech. J., 1950). I will talk some mathematical theory of quasineutrality for semiconductor and plasma. Some rigorous convergence results on structure stability are reviewed and some new results obtained recently will be given.

Stability of boundary layers for Navier-Stokes Poisson system in half-space

Xin Xu (徐鑫)

Institute of Applied Physics and Computational Mathematics

E-mail address: xuxinaboy@126.com

Abstract: We are concerned with the quasi-neutral and zero-viscosity limits of Navier-Stokes-Poisson equations in the half-space. By means of asymptotic analysis with multiple scales,we construct an approximate solution of the Navier-Stokes-Poisson equations, and establish the stability of the boundary layer approximations by conormal energy estimate.

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