Geodesic
Partial Differential Equations/Optimal Control
A Hamilton–Jacobi PDE in the space of measures and its associated compressible Euler equations
[Une EDP de Hamilton–Jacobi dans lʼespace des mesures et ses équations dʼEuler compressibles associées]

Présenté par : the Editorial Board

Feng, Jin1
1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 973-976.

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We introduce a class of action integrals defined over probability-measure-valued path space. Minimal action exists in this context and gives weak solution to a compressible Euler equation. We prove that the Hamilton–Jacobi PDE associated with such variational formulation of Euler equation is well posed in viscosity solution sense.

Nous introduisons une classe dʼintégrales dʼaction définies sur lʼespace des chemins à valeurs mesures de probabilité. Dans ce contexte lʼaction minimale existe et donne une solution faible dʼune équation dʼEuler compressible. Nous montrons que lʼéquation de Hamilton Jacobi associʼee à la formulation variationnelle de lʼéquation dʼEuler est bien posée dans le sens des solutions de viscosité.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.08.013

Feng, Jin 1

1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA 
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Feng, Jin. A Hamilton–Jacobi PDE in the space of measures and its associated compressible Euler equations. Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 973-976. doi : 10.1016/j.crma.2011.08.013. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.08.013/

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