Global L₂-solutions of stochastic Navier-Stokes equations

الأصل · EN

This paper concerns the Cauchy problem in Rᵈ for the stochastic Navier-Stokes equation ∂ₜu=Δu-(u,∇)u-∇ p+f(u)+ [(σ,∇)u-∇ p+g(u)]∘ W, u(0)=u₀, divu=0, driven by white noise W. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier-Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaos-based criterion for the existence and uniqueness of a strong global solution of the Navier-Stokes equations is established.