会议介绍

The existence of the global smooth solution of n-dimensional incompressible Navier-Stokes equations is one of the most difficult problems in applied mathematics. As it is well known, n-dimensional nonlinear systems of fluid dynamics equations play very important roles in engineering, industry and applied mathematics. These problems are closely related to accurate weather forecast, geographical exploration, navigation, inner and outer space exploration, etc.

The main purpose of this international conference is to bring together worldwide leading experts as well as other mathematicians, particularly young researchers, to foster the advances of mathematical theory and applications of nonlinear systems of fluid dynamics equations, to couple together traditional ideas, methods, results and new innovation ideas to create new mathematics, and to explore positive solutions to worldwide difficult problems, such as

* the regularity of global weak solutions of the Navier-Stokes equations and related equations, without making any additional assumptions

* smoothness of the global weak solutions of the Navier-Stokes equations and related equations

* necessary and sufficient conditions for global weak solution to be global smooth solutions

* the possibility to couple together all recent ideas, methods, techniques and results to accomplish the existence of the global smooth solution of n-dimensional incompressible Navier- Stokes equations, for all n ≥ 3

* to find very different ideas, methods, techniques to solve many other interesting and important problems in fluid dynamics, to prove existence of global smooth solutions of fluid dynamics equations.

Another very important goal is to celebrate the 80th birthday of Professor Boling Guo, a highly respected member of Chinese Academy of Sciences.

The mathematical model equations to be covered:

* The n-dimensional Navier-Stokes equations and related equations * n-dimensional magnetohydrodynamics equations * n-dimensional Newton-Boussinesq equations * two-dimensional nonlocal quasi-geostrophic equations

* n-dimensional Camassa-Holms-Burgers equations * equations closely related to Korteweg-de Vries equations or Korteweg-de Vries-Burgers equation

Topics to be included:

* existence of global smooth solutions * long time asymptotic behaviors of L2 and other norms of global solutions * regularity of global weak solutions * uniqueness of global weak solution * blow up phenomena of weak solutions * existence of global attractors * computation of Hausdorff dimension of the global attractors

组织者

Shijin Ding, South China Normal University

Linghai Zhang, Lehigh University, USA

参会人员

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