Random electrostatic fluctuations with fixed intensity and vanishing spatial correlation produce velocity diffusion in the Vlasov-Poisson limit, proving a deterministic Vlasov-Fokker-Planck equation.
Scaling Limit and Large Deviation for 3D Globally Modified Stochastic Navier-Stokes Equations with Transport Noise
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We consider the globally modified stochastic (hyperviscous) Navier-Stokes equations with transport noise on 3D torus. We first establish the existence and pathwise uniqueness of the weak solutions, and then show their convergence to the solutions of the deterministic 3D globally modified (hyperviscous) Navier-Stokes equations in an appropriate scaling limit. Furthermore, we prove a large deviation principle for the stochastic globally modified hyperviscous system.
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A scaling limit for Vlasov equations with electrostatic fluctuations
Random electrostatic fluctuations with fixed intensity and vanishing spatial correlation produce velocity diffusion in the Vlasov-Poisson limit, proving a deterministic Vlasov-Fokker-Planck equation.