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Uniform Approximation of 2D Navier-Stokes Equations with Vorticity Creation by Stochastic Interacting Particle Systems

Francesco GrottoEliseo LuongoMario Maurelli
Dec 2022
摘要
We consider a stochastic interacting particle system in a bounded domain withreflecting boundary, including creation of new particles on the boundaryprescribed by a given source term. We show that such particle systemapproximates 2d Navier-Stokes equations in vorticity form and impermeableboundary, the creation of particles modeling vorticity creation at theboundary. Kernel smoothing, more specifically smoothing by means of the Neumannheat semigroup on the space domain, allows to establish uniform convergence ofregularized empirical measures to (weak solutions of) Navier-Stokes equations.
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