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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wei Wang & Jianliang Zhai & Tusheng Zhang, 2022. "Stochastic Two-Dimensional Navier–Stokes Equations on Time-Dependent Domains," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2916-2939, December.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:4:d:10.1007_s10959-021-01150-0
    DOI: 10.1007/s10959-021-01150-0
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    References listed on IDEAS

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    1. Sritharan, S.S. & Sundar, P., 2006. "Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1636-1659, November.
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