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Vanishing viscosity limit II

  • 演讲者:王晓明(南方科技大学)

  • 时间:2021-01-20 14:00-15:00

  • 地点:慧园3栋518(腾讯会议 ID 192 906 394)

Abstract: Many physically important fluids are viscous but their viscosities are small leading to the idealized approximation of inviscid fluid. A long standing open mathematical problem is the validity of this approximation from small viscosity to zero viscosity. From the PDE point of view, the question is the convergence of solutions to the Navier-Stokes equations to those of the inviscid Euler fluid equations. The difficulty is related to the existence of a thin boundary layer discovered by L. Prandtl more than 100 years ago. And his discovery led to the beginning of the field of singular perturbation, a fundamental quantitative tool in science and engineering. I will survey a few historical important results, offer a few examples that are accessible to undergraduates with knowledge of undergraduate PDEs, and point out the key difficulty associated with the Prandtl approach. All are welcome.