We prove the existence of stochastic processes solving the deterministic Euler equations for an inviscid fluid on the 2D torus. In [20] Kuksin obtained this result by approximating the Euler equations by the stochastic Navier-Stokes equations with viscous term −ν\Delta v and intensity of the noise vanishing as √ν; then in the limit as ν → 0 non trivial stationary processes solving the deterministic Euler equations were obtained. In this paper we modify the approximating viscous equations by considering a dissipative term ν(−\Delta)^pv for p > 0 and p\neq 1. We prove that the Eulerian limit process depends on the noise and on the parameter p; hence the Eulerian limits obtained for p\neq 1 are different from those obtained by Kuksin when p = 1.

On 2D Eulerian limits à la Kuksin

Benedetta Ferrario
2023-01-01

Abstract

We prove the existence of stochastic processes solving the deterministic Euler equations for an inviscid fluid on the 2D torus. In [20] Kuksin obtained this result by approximating the Euler equations by the stochastic Navier-Stokes equations with viscous term −ν\Delta v and intensity of the noise vanishing as √ν; then in the limit as ν → 0 non trivial stationary processes solving the deterministic Euler equations were obtained. In this paper we modify the approximating viscous equations by considering a dissipative term ν(−\Delta)^pv for p > 0 and p\neq 1. We prove that the Eulerian limit process depends on the noise and on the parameter p; hence the Eulerian limits obtained for p\neq 1 are different from those obtained by Kuksin when p = 1.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1474495
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact