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Stochastic 2D Navier-Stokes equations on time-dependent domains
Wei Wang, Jianliang Zhai, Tusheng Zhang · 2021-05-28 · via math.PR updates on arXiv.org

We establish the existence and uniqueness of solutions to stochastic 2D Navier-Stokes equations in a time-dependent domain driven by Brownian motion. A martingale solution is constructed through domain transformation and appropriate Galerkin approximations on time-dependent spaces. The probabilistic strong solution follows from the pathwise uniqueness and the Yamada-Watanable theorem.

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