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Jared Speck Vanderbilt University

September 14, 2023, Thursday, 3:30-4:30pm, Hill 705

THE STRUCTURE OF THE MAXIMAL DEVELOPMENT FORSHOCK-FORMING 3D COMPRESSIBLE EULER SOLUTION

I will discuss my ongoing series of works with L. Abbrescia on 3D compressible Euler flow. In these works, we derive the complete structure of a localized portion of the maximal development for opensets of initial data without symmetry, irrotationality, or isentropicity assumptions. In particular, we describe the full structure of a localized portion of the singular set, where the solution’s gradient blows up in a shock singularity, as well as the emergence of a localized piece of a Cauchy horizon from the singularity. Our work builds on Christodoulou’s breakthrough monographs on irrotational solutions and my prior works with J. Luk, which revealed an implicit portion of the singular set. The key new ingredients are rough foliations of spacetime adapted to the shape of the boundary and a geo-analytic framework that yields suitable estimates on the foliations. Finally, I will discuss some of the many open problems in the field.