On the convergence of stochastic transport equations to a deterministic parabolic one. (English) Zbl 1456.35242
Summary: A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of STLE to the solution of a deterministic parabolic equation. Existence and uniqueness for STLE are also discussed. Our method works in dimension \(d\ge 2\); the case \(d=1\) is also investigated but no conclusive answer is obtained.
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35Q49 | Transport equations |
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