Local existence of strong solutions to the stochastic Navier-Stokes equations with $L^{p}$ data

Igor Kukavica; Fanhui Xu

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arXiv · 2110.07091

Local existence of strong solutions to the stochastic Navier-Stokes equations with $L^{p}$ data

Igor Kukavica·Fanhui Xu

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Abstract

For the stochastic Navier-Stokes equations with a multiplicative white noise on ${\mathbb T}^{3}$, we prove that there exists a unique strong solution locally in time when the initial datum belongs to $L^p(\Omega; L^p)$ for $p>3$.

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Igor Kukavica, Fanhui Xu. 2021-10-14. Local existence of strong solutions to the stochastic Navier-Stokes equations with $L^{p}$ data. https://arxiv.org/abs/2110.07091

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