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arxiv: 1102.3076 · v2 · pith:J7UK2EASnew · submitted 2011-02-15 · 🧮 math.FA · math.PR

L^(p)-solutions of the stochastic transport equation

classification 🧮 math.FA math.PR
keywords equationtransportlinearsolutionsstochasticassumptionsconsiderdeterministic
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We consider the stochastic transport linear equation and we prove existence and uniqueness of weak $L^{p}-$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 It\^o-Ventzel-Kunita formula (see 15) and the theory of Lions-DiPerna on transport linear equation (see 9).

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