We prove a uniqueness result for the stochastic transport linear equation (STLE), without any or BV hypothesis on the coefficient, which is needed for the corresponding deterministic equation. We use Wiener chaos decomposition to pass from the STLE to a deterministic second-order transport equation with uniqueness property.
On prouve un résultat dʼunicité pour lʼéquation de transport linéaire stochastique (STLE), sans aucune hypothèse de type ou BV sur le coefficient, qui est nécessaire pour lʼéquation déterministe correspondante. On utilise la décomposition en chaos de Wiener pour passer de la STLE à une équation de transport du second ordre déterministe avec la propriété dʼunicité.
Accepted:
Published online:
Mario Maurelli 1
@article{CRMATH_2011__349_11-12_669_0, author = {Mario Maurelli}, title = {Wiener chaos and uniqueness for stochastic transport equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {669--672}, publisher = {Elsevier}, volume = {349}, number = {11-12}, year = {2011}, doi = {10.1016/j.crma.2011.05.006}, language = {en}, }
Mario Maurelli. Wiener chaos and uniqueness for stochastic transport equation. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 669-672. doi : 10.1016/j.crma.2011.05.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.006/
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