고등과학원 특강입니다.

TIME: July 08 (Thu), 2021, 10:00-11:00/ 14:00-15:00
SPEAKER: 채동호 (중앙대)
TITLE: Mathematical Challenges in Fluid Mechanics I, II

Abstract : In this lecture we discuss some mathematical problems in the fluid mechanics. Many of the physical systems are described partial differential equations, and the mathematical study of these equations could have important and direct physical significances. In general, in the cases when the equations are nonlinear and nonlocal systems the study of solutions to the equations are much more difficult than the other cases. The fluid equations we are interested in corresponds to these cases. Among others we are particularly interested in the problem of singularities in the incompressible Navier-Stokes and the Euler equations. We emphasize that singularities in the solution of partial differential equations has direct physical importance in many cases. One fashionable example is the singularity of the Einstein field equation, which is nothing but the black hole. The other one is the singularities in the compressible Euler equations, which correspond to the shock waves. The singularities in the Navier-Stokes and the Euler equations are less understood than the two above cases. In the rest part of this lecture we introduce, in general terms, the problem of singularities in the fluids. In the second part we focus on some of the recent studies on the problem, related to the scenario of Type I singularities.

Zoom Link : https://us02web.zoom.us/j/89261183867