Conservation of total vorticity for a 2D stochastic Navier-Stokes equation
Summary: We consider \(N\) point vortices whose positions satisfy a stochastic ordinary differential equation on \(\mathbb R^{2N}\) perturbed by spatially correlated Brownian noise. The associated signed point measure-valued empirical process turns out to be a weak solution to a stochastic Navier-Stokes equation (SNSE) with a state-dependent stochastic term. As the number of vortices tends to infinity, we obtain a smooth solution to the SNSE, and we prove the conservation of total vorticity in this continuum limit.
scientific article; zbMATH DE number 6012972
scientific article