Remarkable integral identities for 3D compressible Euler flow

Remarkable integral identities for 3D compressible Euler flow

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Jared Speck, Vanderbilt University

Zoom link:

https://princeton.zoom.us/j/514560553

In recent joint work with L. Abbrescia, we derived some new, coercive integral identities for solutions
to the compressible Euler equations in 3D with vorticity and entropy. The error terms in the
identities exhibit remarkable null structures and enjoy unexpected regularity, which in total allows
one to use the full power of the geometric vectorfield method on any region that is globally hyperbolic
with respect to the acoustical metric. The integral identities hold in particular on regions covered
by double-acoustically null foliations. In this talk, I will discuss the derivation of these identities
and their implications for the geometry and regularity of solutions, the formation of shocks, the
structure of the maximal classical development of the data, and for controlling solutions whose state
along a pair of intersecting characteristic hypersurfaces is known.