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Local Well-Posedness of Strong Solutions to the Three-Dimensional Compressible Primitive Equations

Published version
Peer-reviewed

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Abstract

This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, unique, and depend continuously on the initial data, for a short time in two cases: with gravity but without vacuum, and with vacuum but without gravity. We also introduce the free boundary problem for the compressible primitive equations.

Description

Funder: Einstein Stiftung Berlin; doi: http://dx.doi.org/10.13039/501100006188


Funder: Fondation de l’École Polytechnique; doi: http://dx.doi.org/10.13039/501100009454

Keywords

math.AP, math.AP, physics.flu-dyn, physics.geo-ph, 35Q30, 35Q35, 76N10

Journal Title

Archive for Rational Mechanics and Analysis

Conference Name

Journal ISSN

0003-9527
1432-0673

Volume Title

241

Publisher

Springer Science and Business Media LLC
Sponsorship
Division of Mathematical Sciences (1516866)
Office of Naval Research Global (N00014-15-1-2333)
NSF grant number DMS-1516866 ONR grant N00014-15-1-2333 Einstein Stiftung/Foundation-Berlin, Einstein Visiting Fellowship No. EVF-2017-358