#### 2017 Academic Year on PDE

#### 2017 Academic Year on PDE

#### Introduction

The differential equation is an important subject in mathematics, the research problem in this academic activities will be all types of the partial differential equations, such as shock interface of high dimensional Euler equations, incompressible Euler equations, compressible and incompressible Navier-Stokes equations, and the study of singular solution for elliptic and parabolic equation. The research direction has attracted many famous mathematicians in the world, such as Luis Caffarelli, Terence Tao, J.Bourgain and Anver Friedman and other famous mathematicians.

The academic year consists of the Silk Road Center PDE mathematical activities jointly with Chinese Mathematical Society, and three thematic activities will be carried out in 2017, cultivate a group of high level young talents and publish some high level papers through these activities, promote the development of related research areas.

Seminar on Incompressible Fluid Dynamics Equations

The most important subject of the three-dimensional incompressible Navier-Stokes equation is the existence and uniqueness of the global solution of the initial function with finite smooth energy. Except that Navier-Stokes equation has its distinctive physical background, the corresponding nonlinear term has a good structure, the known invariants is not sufficient to overcome the singularity arising from the high-frequency interaction, it is more difficult to control the behavior of Navier-Stokes equation at fine scale than coarse scale, and the supercritical makes it impossible to control the nonlinear interaction on fine scale. Even for Navier-Stokes equations with axisymmetric rotation, the problem is still open, the study of this problem and other related problems will promote the development of study for differential equations.

Seminar on Nonlinear Diffusion Equations and Nonlinear Elliptic Equations

Nonlinear parabolic, hyperbolic and evolution equations with random terms, the existence, uniqueness and structure of solutions for these problems are important issues. Especially the study of singular structure of solutions for the nonlinear evolution equations, even with smooth initial value, the solution may also be singular at finite time, it is necessary to study the cause of singularity, the position of singularity, the time of occurrence, the possibility of continuation and the properties after the occurrence of singularity.

Seminar on Free Boundary Problems

The free boundary problem involves all types of partial differential equations, such as the shock interface of the high dimensional Euler equation and the vacuum interface of the compressible Navier-Stokes equation, it is necessary to study the smoothness of the free boundary.

Academic year organizational committees

Liqun Zhang(person responsible), Daomin Cao, Guiqiang Chen, Feimin Huang, ZHouping Xin, Ping Zhang.