$L^{p}-$solutions of the stochastic transport equation

Details $L^{p}-$solutions of the stochastic transport equation $L^{p}-$solutions of the stochastic transport equation

2011-02-15

arxiv.org/abs/1102.3076v2

Mathematics

Functional Analysis

Changed Intrododuction, bibliography

Scientific paper

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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