Title: Partial Differential Equations and Applied Mathematics Seminar (2016.12.8)

Author: CMAC

Date: 2016-12-05 (21:36)

Date/Time: Dec. 8th,Thur., 4:00 ~ 5:00 PM

Location: Science Building #254 Yonsei University

Speaker: Prof. Hideyuki Miura

Affiliation: Tokyo Institute of Technology, Department of Mathematics and Computing Sciences, Tokyo, Japan

Title: The growth of the vorticity gradient for the two-dimensional Euler flows on domains with corners

Abstract:

We consider the two-dimensional Euler equations in non-smooth domains with corners. It is shown that if the angle of the corner is strictly less than π/2, the Lipschitz estimate of the vorticity at the corner is at most single exponential growth and the upper bound is sharp. For the corner with the angle between π/2 and 2π except π, we construct an example of the vorticity which loses continuity instantaneously. This is a joint work with Tsubasa Itoh and Tsuyoshi Yoneda