Conservation of Total Vorticity for a 2D Stochastic Navier Stokes Equation | Zendy

Peter Kotelenez | Zendy; Bradley T. Seadler | Zendy

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Conservation of Total Vorticity for a 2D Stochastic Navier Stokes Equation

Author(s) -

Peter Kotelenez,

Bradley T. Seadler

Publication year - 2011

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2011/862186

Subject(s) - mathematics , stochastic differential equation , vorticity , mathematical analysis , vortex , brownian motion , limit (mathematics) , infinity , vorticity equation , ordinary differential equation , measure (data warehouse) , navier–stokes equations , brownian noise , differential equation , physics , white noise , mechanics , compressibility , statistics , database , computer science

We consider point vortices whose positions satisfy a stochastic ordinary differential equation on ℝ2 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

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