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On a class of stochastic transport equations for \(L^2_{\mathrm{loc}}\) vector fields. (English) Zbl 1391.60157

Summary: We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients. Asking only boundedness of the divergence of the coefficients (a classical condition in both the deterministic and stochastic setting), we can lower the integrability regularity required in known results on the coefficients themselves and on the initial condition, and still prove uniqueness of solutions.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35F10 Initial value problems for linear first-order PDEs
60H30 Applications of stochastic analysis (to PDEs, etc.)
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