Martingale solutions for stochastic active scalar equations perturbed by non-trace class noise

2014/05/28 by Rongchan Zhu, Xiangchan Zhu · 1 voice
Economics, Econometrics and Finance · Engineering · Mathematics · #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stochastic processes and financial applications

paper · doi:10.1142/s0219025714500106

openalex publication_date 2014/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

In this paper we prove the existence of martingale solutions for the 2D stochastic fractional vorticity Navier–Stokes equation driven by space-time white noise for α ∈ (½, 1] and the 2D stochastic quasi-geostrophic equation on 𝕋 2 for α ∈ (0, 1] driven by non-trace class noise. We also cover the case driven by non-trace class multiplicative noise for all α ∈ (0, 1].

Citations

• Random attractor associated with the quasi-geostrophic equation

Discussions

• What happens when fluid equations are influenced by highly irregular random noise? The authors prove martingale solutions for stochastic models of vorticity, Navier–Stokes equations, and quasi-geostr [bsky, 3 points, 0 comments]

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