Dongho Chae: On the self-similar blow-up for the compressible Euler equations
Dongho Chae (Chung-Ang University, Korea) will give a seminar talk entitled
On the self-similar blow-up for the compressible Euler equations
Abstract: The problem of ﬁnite time blow-up/global regularity of the 3D incompressible Euler equations is an outstanding problem in mathematical ﬂuid mechanics. On the other hand, the scenario of self-similar type blow-up is a natural candidate of blow-ups in various nonlinear partial differential equations such as the porous medium equation and the nonlinear Schrödinger equations. We also mention that for the closely related incompressible Navier-Stokes equations the question of self-similar blow-up was raised by J. Leray in 1930, and was negatively answered by J. Necas, M. Ruzicka and V. Sverak in 1996. In this talk we present the progress of study during the last several years on the self-similar blow-up for the Euler equations.