Zero-noise dynamics after collapse for three point vortices

Grotto, Francesco; Romito, Marco; Viviani, Milo

doi:10.1016/j.physd.2023.133947

Cited by 2 publications

(1 citation statement)

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“…including self-interaction terms induced from the boundary effects; this is necessary for the system to satisfy in a weak form (as in [44]) the 2-dimensional Euler equations. We refer to [38, chapter 4] for a general introduction to the topic, to [15,22,25,26,30] on the issue of wellposedness of the dynamics and vortex collisions, and to [23,24,[27][28][29]36] on the statistical mechanics point of view. Self-interactions diverge logarithmically at ∂D, and this prevents us to include them in our model because the Brownian part of the dynamics (which we must include to model viscosity) might drive particles onto the boundary causing blow-up of the dynamics at finite time.…”

Section: Diffusion Processes and Reflecting Boundariesmentioning

confidence: 99%

Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems

Grotto,

Luongo,

Maurelli

2023

Nonlinearity

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We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier–Stokes equations.

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