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

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Exploiting recent regularity estimates for the Monge-Ampère equation, under some suitable assumptions on the initial data we prove globalin-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domains.

Original language	English (US)
Pages (from-to)	1251-1268
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	34
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2014.34.1251
State	Published - Apr 2014

Keywords

Optimal transportation
Semigeostrophic equations

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2014.34.1251

Cite this

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title = "A global existence result for the semigeostrophic equations in three dimensional convex domains",

abstract = "Exploiting recent regularity estimates for the Monge-Amp{\`e}re equation, under some suitable assumptions on the initial data we prove globalin-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domains.",

keywords = "Optimal transportation, Semigeostrophic equations",

author = "Luigi Ambrosio and Maria Colombo and {De Philippis}, Guido and Alessio Figalli",

year = "2014",

month = apr,

doi = "10.3934/dcds.2014.34.1251",

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publisher = "Southwest Missouri State University",

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AU - Ambrosio, Luigi

AU - Colombo, Maria

AU - De Philippis, Guido

AU - Figalli, Alessio

PY - 2014/4

Y1 - 2014/4

N2 - Exploiting recent regularity estimates for the Monge-Ampère equation, under some suitable assumptions on the initial data we prove globalin-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domains.

AB - Exploiting recent regularity estimates for the Monge-Ampère equation, under some suitable assumptions on the initial data we prove globalin-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domains.

KW - Optimal transportation

KW - Semigeostrophic equations

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

Abstract

Keywords

ASJC Scopus subject areas

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