Stochastic Two-Dimensional Navier–Stokes Equations on Time-Dependent Domains

Wei Wang (), Jianliang Zhai () and Tusheng Zhang ()
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Wei Wang: University of Science and Technology of China
Jianliang Zhai: University of Science and Technology of China
Tusheng Zhang: University of Science and Technology of China

Journal of Theoretical Probability, 2022, vol. 35, issue 4, 2916-2939

Abstract: Abstract We establish the existence and uniqueness of solutions to stochastic Two-Dimensional Navier–Stokes equations in a time-dependent domain driven by Brownian motion. A martingale solution is constructed through domain transformation and appropriate finite-dimensional approximations on time-dependent spaces. The probabilistic strong solution follows from the pathwise uniqueness and the Yamada–Watanabe theorem. Because the state space of the solution changes with time, we need to deal with the various problems caused by the lack of appropriate chain rules/Itô’s formula, apart from the nonlinearity of the Navier–Stokes equation.

Keywords: Stochastic Navier–Stokes equations; Time-dependent domain; Tightness; Yamada–Watanabe theorem; 60H15; 35Q30; 76D05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01150-0

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