Seminar

We will discuss local well-posedness and ill-posedness results of some active scalar equations, including 2D incompressible Euler equations and the SQG equation. We will discuss how one can obtain instantaneous growth of solutions using a perturbation of a steady initial data as well as making use of unboundedness of the Riesz transform in $L^\infty$. We will then discuss the first result of an instantaneous gap loss of Sobolev regularity for 2D Euler. Namely, we will describe a construction of initial vorticity for the 2D Euler equations that belongs to the Sobolev space $H^\beta$, $\beta \in (0,1)$ which gives rise to a unique global-in-time solution that instantaneously leaves not only $H^\beta$, but also $H^{\beta'}$ for every $\beta' >(2-\beta )\beta /(2-\beta^2)$. This is joint work with Diego Cordoba and Luis Martinez-Zoroa.

Meeting ID: 998 5718 9855

Passcode: 983468

Link: https://msri.zoom.us/j/99857189855?pwd=LzRFR2tPN1cydWJNZEZkclZGV2lpQT09

Instantaneous Gap Loss of Sobolev Regularity for the 2D Incompressible Euler Equations 330 KB application/pdf

FD2 Reunion Seminar: Instantaneous Gap Loss Of Sobolev Regularity For The 2D Incompressible Euler Equations