Correction to: Burst of Point Vortices and Non-uniqueness of 2D Euler Equations

Pappalettera, Umberto

doi:10.1007/s00205-022-01814-z

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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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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Effect of Transport Noise on Kelvin–Helmholtz Instability

Flandoli,

Morlacchi,

Papini

2023

Mathematics of Planet Earth

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The effect of transport noise on a 2D fluid may depend on the space-scale of the noise. We investigate numerically the dissipation properties of very small-scale transport noise. As a test problem we consider the Kelvin-Helmholtz instability and we compare the inviscid case, the viscous one, both without noise, and the inviscid case perturbed by transport noise. We observe a partial similarity with the viscous case, namely a delay of the instability.

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Correction to: Burst of Point Vortices and Non-uniqueness of 2D Euler Equations

Cited by 2 publications

References 1 publication

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

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

Effect of Transport Noise on Kelvin–Helmholtz Instability

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