Analysis Seminar

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On stable implosions

Speaker: Vlad Vicol, NYU

Location: Warren Weaver Hall 1302

Date: Thursday, September 18, 2025, 11 a.m.

Synopsis:

We exhibit a new class of implosion profiles for the full compressible Euler equations. Specifically, for any value of the adiabatic exponent, we construct a discretely infinite sequence of implosions that are smooth (real analytic before collapse) and have an explicit similarity exponent (as opposed to Guderley's). The first profile in this sequence (the ''ground state'') possesses remarkable stability properties, even outside of spherical symmetry, making it an ideal benchmark for Euler codes.

This is joint work with J. Chen (U Chicago) and S. Shkoller (UC Davis).