#### Workshop on Partial Differential Equations 2017

#### Workshop on Partial Differential Equations 2017

#### 活动内容

Organizers: Feimin Huang, Yi Wang and Yong Wang,

Place: Room 205, South Building, AMSS

Title: Nongauge invariant cubic nonlinear Schredinger equations

Speaker：Prof. Nakao Hayashi, Osaka University, Japan

Time：2017.09.09, 2:00-3:00 pm

Place：South Building, Room 205

Abstract: It is known that in the one dimensional case, the cubic type nonlinearities are critical with respect to the large time asymptotic behavior of solutions. Gauge invariant cubic nonlinear Schredinger equation was studied by many authors. In this talk, we consider the Cauchy problem for the cubic nongauge invariant nonlinear Schredinger equation and present a sufficient condition which gives us asymptotic behavior of small solutions.

Title：Behaviors of Navier-Stokes-Fokker-Planck Equations

Speaker：Prof. Hailiang Li, Capital Normal University

TIme：2017.09.09, 3:00-4:00 pm

Place：South Building, Room 205

Title: Quasi-one-dimensional approximation of two-dimensional steady supersonic exothermically reacting Euler flows

Speaker：Prof. Yongqian Zhang，Fudan University

Time：2017.09.09, 4:00-5:00 pm

Place：South Building, Room 205

Abstract：We are concerned with quasi-one-dimensional approximation of gas flow between the boundary and strong contact discontinuity in two-dimensional steady supersonic exothermically reacting Euler flow over Lipschitz walls. When the total variation of both initial data and the slope of Lipschitz walls is small enough, We first establish the global existence of entropy solutions with strong contact discontinuity, then prove that the difference between the average of weak solution and the solution of quasi-one-dimensional system can be bounded by the square of the total variation of both initial data and the slope of Lipschitz walls.