Lp-solutions of the stochastic transport equation

Lp-solutions of the stochastic transport equation

We consider the stochastic transport linear equation and we prove existence and uniqueness of weak -solutions. Moreover, we obtain a representation of the general solution and a Wong-Zakai principle for this equation. We make only minimal assumptions, similar to the deterministic problem. The proof...

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Veröffentlicht in:Random operators and stochastic equations 2013-06, Vol.21 (2), p.125-134
Hauptverfasser: Catuogno, Pedro, Olivera, Christian
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Itô formula
Lions–DiPerna theory
Stochastic models
Stochastic perturbation
transport equation
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Beschreibung
Zusammenfassung:We consider the stochastic transport linear equation and we prove existence and uniqueness of weak -solutions. Moreover, we obtain a representation of the general solution and a Wong-Zakai principle for this equation. We make only minimal assumptions, similar to the deterministic problem. The proof is supported on the generalized Itô–Ventzel–Kunita formula and the theory of Lions–DiPerna on transport linear equation.
ISSN:0926-6364
1569-397X
DOI:10.1515/rose-2013-0007