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arXiv · 2504.05648

The stochastic Navier-Stokes equations with general $L^{3}$ data

Mustafa Sencer Aydın·Igor Kukavica·Fanhui Xu
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Abstract

We consider the stochastic Navier-Stokes equations with multiplicative noise with critical initial data. Assuming that the initial data $u_0$ belongs to the critical space $L^{3}$ almost surely, we construct a unique local-in-time probabilistically strong solution. We also prove an analogous result for data in the critical space~$H^\frac{1}{2}$.

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Mustafa Sencer Aydın, Igor Kukavica, Fanhui Xu. 2025-04-08. The stochastic Navier-Stokes equations with general $L^{3}$ data. https://arxiv.org/abs/2504.05648

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