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arXiv · 2504.13468

Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains

Ping Chen·Tianyi Pan·Tusheng Zhang
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Abstract

In this paper, we establish the strong($H^1$) well-posedness of the two dimensional stochastic Navier-Stokes equation with multiplicative noise on moving domains. Due to the nonlocality effect, this equation exhibits a ``piecewise" variational setting. Namely the global well-posedness of this equation is decomposed into the well-posedness of a family of stochastic partial differential equations(SPDEs) in the variational setting on each small time-interval. We first examine the well-posedness on each time interval, which does not have (nonhomogeneous) coercivity. Subsequently, we give an estimate of lower bound of length of the time-interval, which enables us to achieve the global well-posedness.

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Ping Chen, Tianyi Pan, Tusheng Zhang. 2025-04-18. Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains. https://arxiv.org/abs/2504.13468

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