h-Principles for the Incompressible Euler Equations

A. Choffrut

Research output: Contribution to journalArticlepeer-review

Abstract

In Dissipative Euler Flows and Onsager’s Conjecture. arxiv.1205.3626, preprint, 2012, De Lellis and Székelyhidi construct Hölder continuous, dissipative (weak) solutions to the incompressible Euler equations in the torus T3. The construction consists of adding fast oscillations to the trivial solution. We extend this result by establishing optimal h-principles in two and three space dimensions. Specifically, we identify all subsolutions (defined in a suitable sense) which can be approximated in the H −1-norm by exact solutions. Furthermore, we prove that the flows thus constructed on T3 are genuinely three-dimensional and are not trivially obtained from solutions on T2.

Original languageEnglish
Pages (from-to)133-163
Number of pages31
JournalArchive for Rational Mechanics and Analysis
Volume210
Issue number1
Early online date24 May 2013
DOIs
Publication statusPublished - Oct 2013

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