Almost global existence for the stochastic Navier-Stokes equations with small H^1/2 data

2025/01/17 by Mustafa Sencer Aydın, Igor Kukavica, Aydın, Mustafa Sencer +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2501.10331

openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in H^1/2(\mathbbT³). We prove that the solution exists globally in time with probability arbitrarily close to~1 if the initial data and noise are sufficiently small. If the noise is not assumed to be small, then the solution is global on a sufficiently small deterministic time interval with probability arbitrarily close to~1.

Cited by

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

Related

• Global existence of the stochastic Navier-Stokes equations in L³ with small data
• The stochastic Navier-Stokes equations with general L³ data
• Local existence of strong solutions to the stochastic Navier-Stokes equations with L^p data
• Global L₂-solutions of stochastic Navier-Stokes equations
• Local and global strong solutions to the stochastic incompressible Navier-Stokes equations in critical Besov space