Stochastic Two-Dimensional Navier–Stokes Equations on Time-Dependent Domains
Stochastic Two-Dimensional Navier–Stokes Equations on Time-Dependent Domains
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DOI：
10.1007/s10959-021-01150-0
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发表时间：
2022-01
影响因子：
0.8
通讯作者：
Wei Wang;Jianliang Zhai;Tusheng Zhang
中科院分区：
文献类型：
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作者：
Wei Wang;Jianliang Zhai;Tusheng Zhang
我们在布朗运动驱动的瞬态域中建立了随机二维纳维-斯托克斯方程解的存在性和唯一性。鞅解是通过域变换和时间相关空间上的适当有限维近似来构造的。概率强解由路径唯一性和山田渡边定理得出。由于解的状态空间随时间变化，除了纳维-斯托克斯方程的非线性之外，我们还需要处理由于缺乏适当的链规则/伊藤公式而引起的各种问题。
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.