Solutions of the fully compressible semi-geostrophic system

M. J. P. Cullen, D. K. Gilbert, Beatrice Pelloni

Research output: Contribution to journalArticle

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Abstract

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.
Original languageEnglish
Pages (from-to)591-625
Number of pages35
JournalCommunications in Partial Differential Equations
Volume39
Issue number4
DOIs
Publication statusPublished - 2014

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