On blow up for the defocusing NLS and three dimensional viscous compressible fluids

Abstract: Global existence and scattering for the defocusing nonlinear Schrodinger equation is a celebrated result by Ginibre-Velo in the early 80’s in the strictly energy sub critical case, and Bourgain in 94 in the energy critical case. In the energy super critical setting, the defocusing energy is conserved and controls the energy norm, but this is too weak to conclude to global existence which yet had been conjectured by many and confirmed by numerical computations. This is a canonical super critical problem which typically arises similarily in fluid mechanics, and there global existence is either completely open or a direct consequence of the existence of additional conservation laws. In this talk based on recent joint works with Merle (IHES), Rodnianski (Princeton) and Szeftel (Paris Sorbonne), I will describe the construction of newsmooth and finite energy highly oscillatory blow up solutions for the defocusing NLS in suitable energy super critical regimes, and explain how these new bubbles are connected to the also new description of implosion mechanisms for viscous three dimensional compressible fluids.

analysis of PDEs

Audience: researchers in the topic

Comments: Here is the poster of this talk: www.dropbox.com/s/3pgqawpbjh20g6m/5th%20PDE%20Seminar.pdf?dl=0

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PDE seminar via Zoom