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Home » Water waves and other interface problems (Part 1): The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach

Seminar

Water waves and other interface problems (Part 1): The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach February 16, 2021 (08:00 AM PST - 09:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Mihaela Ifrim (University of Wisconsin-Madison)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

 

Video

The Compressible Euler Equations In A Physical Vacuum: A Comprehensive Eulerian Approach

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:  This talk is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical interest in this system, the prior work on this problem is limited to Lagrangian coordinates, in high regularity spaces. Instead, the objective of the present work is to provide a new, fully Eulerian approach to this problem, which provides a complete, Hadamard style well-posedness theory for this problem in low regularity Sobolev spaces. In particular we give new proofs for both existence, uniqueness, and continuous dependence on the data with sharp, scale invariant energy estimates, and continuation criterion. This is joint work with Daniel Tataru

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The Compressible Euler Equations In A Physical Vacuum: A Comprehensive Eulerian Approach