The ℎ-principle and the equations of fluid dynamics-Reference-Cited by-同舟云学术

The ℎ-principle and the equations of fluid dynamics

Published:2012-04-26 Issue:3 Volume:49 Page:347-375
ISSN:0273-0979
Container-title:Bulletin of the American Mathematical Society
language:en
Short-container-title:Bull. Amer. Math. Soc.

Author:

De Lellis Camillo,Székelyhidi László

Abstract

In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov’s h h -principle holds in several cases.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/bull/2012-49-03/S0273-0979-2012-01376-9/S0273-0979-2012-01376-9.pdf

Reference86 articles.

1. Non-uniform integrability and generalized Young measures;Alibert, J. J.;J. Convex Anal.,1997

2. Weak convergence and deterministic approach to turbulent diffusion;Bardos, Claude,2000

3. Euler equations for an ideal incompressible fluid;Bardos, K.;Uspekhi Mat. Nauk,2007

4. Remarks on the breakdown of smooth solutions for the 3-D Euler equations;Beale, J. T.;Comm. Math. Phys.,1984

5. A minimality property for entropic solutions to scalar conservation laws in 1+1 dimensions;Blaser, Michael;Comm. Partial Differential Equations,2010

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