[Une EDP de Hamilton–Jacobi dans lʼespace des mesures et ses équations dʼEuler compressibles associées]
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.
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.
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Jin Feng 1
@article{CRMATH_2011__349_17-18_973_0, author = {Jin Feng}, title = {A {Hamilton{\textendash}Jacobi} {PDE} in the space of measures and its associated compressible {Euler} equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {973--976}, publisher = {Elsevier}, volume = {349}, number = {17-18}, year = {2011}, doi = {10.1016/j.crma.2011.08.013}, language = {en}, }
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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