Global existence of the stochastic Navier-Stokes equations in L³ with small data

2024/10/03 by Igor Kukavica, Kukavica, Igor, Fanhui Xu +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2410.02919

openalex publication_date 2024/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L³ data. Namely, we show that for data sufficiently small, there exists a global-in-time strong L³ solution in a space of probability arbitrarily close to~1.

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• The Navier-Stokes equations with transport noise in critical H^1/2 space

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