Analysis Seminar

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Singularities in compressible fluids

Speaker: Gonzalo Cao-Labora, New York University

Location: Warren Weaver Hall 1302

Date: Thursday, September 26, 2024, 11 a.m.

Synopsis:

Finite time singularities for the radially symmetric compressible Euler and Navier-Stokes equations were found in the work of Merle, Raphaël, Rodnianski and Szeftel, based on self-similar imploding profiles. We will explain how to construct such profiles and extend the construction to a different regime of self-similar parameters. In particular, this allows to extend such singularity results to any value of the adiabatic constant, yielding the first self-similar singularity result for monatomic gases. We will also explain how to upgrade the radially symmetric stability analysis to the nonradial case, which yields the first example of singularities with nonradial initial data or with periodic data. The talk is based on joint works with Tristan Buckmaster, Javier Gomez-Serrano, Jia Shi, and Gigliola Staffilani.