Stochastic Transport Equations with Unbounded Divergence

We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients and unbounded divergence. In the first result we assume the drift is L2([0, T ] × Rd) ∩ L([0, T ] × Rd) and the divergence is the locally integrable. In the second result we show that the smoothing acts as a selection criterion when the drift is in L2([0, T ]×Rd)∩L∞([0, T ]×Rd) without any condition on the divergence.

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