# Smooth imploding solutions for a 3D compressible fluid (in-person talk)

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Gonzalo Cao-Labora, MIT
Fine Hall 322

In person and online talk

We will construct exact, smooth self-similar profiles for the 3D isentropic compressible Euler for all values of the adiabatic constant. This builds upon the pioneering work of Merle, Raphaël, Rodnianski and Szeftel (2019) where they showed the existence of such profiles for a set of adiabatic constants where some analytic function does not vanish. We also provide simplified proofs of the linear and non-linear stability around those profiles and use them to construct solutions to the compressible Navier-Stokes equation with constant density near infinity that blow up. This is joint work with Tristan Buckmaster and Javier Gómez-Serrano.