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
Feng, Jin1
1Department 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

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, Volume 349 (2011) no. 17-18, pp. 973-976. doi: 10.1016/j.crma.2011.08.013

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