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arXiv · 2608.27054

Global well-posedness for the 2D stochastic hypoviscous Navier-Stokes equations

Daniel Goodair·Floris Roodenburg
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Abstract

We study stochastic hypoviscous Navier--Stokes equations on the torus with dissipation $(-\Delta)^\gamma$ for $\gamma \in (\frac{1}{2},1]$ and multiplicative noise. Relying on stochastic maximal regularity results for the linear equation, we establish local well-posedness for this problem in arbitrary dimensions with initial data in a range of scaling-critical Besov spaces. With the aid of $L^q$-energy estimates for the vorticity equation, we also prove global well-posedness of the stochastic hypoviscous Navier--Stokes equation in 2D with linear multiplicative noise.

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Daniel Goodair, Floris Roodenburg. 2026-08-27. Global well-posedness for the 2D stochastic hypoviscous Navier-Stokes equations. https://arxiv.org/abs/2608.27054

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