Compressible fluids and singularity formation in supercritical defocusing Schrödinger equations

Abstract: We will discuss recent work with F. Merle, P. Raphael and J. Szeftel, where we studied the problem of global regularity for a defocusing supercritical Schrodinger equation. The corresponding problem had been settled in the affirmative in a long series of works in the sub-critical and energy critical cases and was conjectured by J. Bourgain to have a similar positive answer in the supercritical case. We construct a set of smooth, nicely decaying initial data for which the corresponding solutions blow up in finite time with a highly oscillatory behavior near singularity. The construction proceeds by establishing a link between the Schr¨odinger and the the compressible Euler equations. It also leads to new singularity results for the compressible Euler and Navier–Stokes equations.

analysis of PDEs

Audience: researchers in the topic

MIT PDE/analysis seminar spring 2020

Series comments: At the time of adding this to mathseminars.org, 7 talks had already taken place. Check the website for details and abstracts math.mit.edu/seminars/pde-analysis/

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