no. 11-12
Partial Differential Equations/Probability Theory
Wiener chaos and uniqueness for stochastic transport equation
[Chaos de Wiener et unicité pour lʼéquation de transport stochastique]

Présenté par : the Editorial Board

Maurelli, Mario1
1 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 669-672.

On prouve un résultat dʼunicité pour lʼéquation de transport linéaire stochastique (STLE), sans aucune hypothèse de type W1,1 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.

We prove a uniqueness result for the stochastic transport linear equation (STLE), without any W1,1 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.05.006
Maurelli, Mario 1

1 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy 
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Maurelli, Mario. Wiener chaos and uniqueness for stochastic transport equation. Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 669-672. doi : 10.1016/j.crma.2011.05.006. http://www.numdam.org/articles/10.1016/j.crma.2011.05.006/

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