Comptes Rendus
no. 17-18
Partial Differential Equations/Optimal Control
A Hamilton–Jacobi PDE in the space of measures and its associated compressible Euler equations

Presented by: the Editorial Board

Jin Feng1
1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 973-976.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.08.013

Jin Feng 1

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

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