Global existence of the stochastic Navier-Stokes equations in $L^3$ with small data

Igor Kukavica; Fanhui Xu

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arXiv · 2410.02919

Global existence of the stochastic Navier-Stokes equations in $L^3$ with small data

Igor Kukavica·Fanhui Xu

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Abstract

We address the global-in-time existence and pathwise uniqueness of solutions for the stochastic incompressible Navier-Stokes equations with a multiplicative noise on the three-dimensional torus. Under natural smallness conditions on the noise, we prove the almost global existence result for small $L^{3}$ data. Namely, we show that for data sufficiently small, there exists a global-in-time strong $L^{3}$ solution in a space of probability arbitrarily close to~$1$.

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BibTeX RIS

Igor Kukavica, Fanhui Xu. 2024-10-03. Global existence of the stochastic Navier-Stokes equations in $L^3$ with small data. https://arxiv.org/abs/2410.02919

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