A global existence result for the semigeostrophic equations in three dimensional convex domains

Luigi Ambrosio; Maria Colombo; Guido De Philippis; Alessio Figalli

doi:10.3934/dcds.2014.34.1251

Article Contents

2014, Volume 34, Issue 4: 1251-1268. Doi: 10.3934/dcds.2014.34.1251 open access

This issue Previous Article Preface Next Article Prescription of Gauss curvature on compact hyperbolic orbifolds

A global existence result for the semigeostrophic equations in three dimensional convex domains

1.
Scuola Normale Superiore, Piazza Cavalieri 7, 56123 Pisa
2.
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa
3.
Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, D-53115 Bonn
4.
Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin TX 78712

Received: July 2012

Revised: December 2012

Published online: October 2013

Abstract / Introduction Related Papers Cited by

Abstract

Exploiting recent regularity estimates for the Monge-Ampère equation, under some suitable assumptions onthe initial datawe prove global-in-time existence of Eulerian distributional solutions to the semigeostrophic equationsin 3-dimensional convex domains.

Keywords:

Optimal transportation,
semigeostrophic equations.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 35J60, 76B03, 86A10.

Citation:

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References

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