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              -White noise solution to 2D stochastic Euler equations

Flandoli, Franco; Luo, Dejun

doi:10.1007/s00440-019-00902-8

Cited by 17 publications

(2 citation statements)

References 24 publications

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“…While in [ 12 ] the authors prove the existence and pathwise uniqueness of a distributional solution in , in this paper we are concerned with the existence of a strong solution and give conditions under which the solution enjoys smoothness properties. 1 In [ 25 ], a random point vortices system is used to construct a so-called -white noise solution. Local well-posedness and a Beale-Kato-Majda blow-up criterion for the three-dimensional case in the space has been obtained in [ 18 ].…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for a stochastic 2D Euler equation with transport noise

Crisan

Lang

2022

Stoch PDE: Anal Comp

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We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz.

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Section: Introductionmentioning

confidence: 99%

Well-posedness for a stochastic 2D Euler equation with transport noise

Crisan

Lang

2022

Stoch PDE: Anal Comp

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“…We also recall that stochasticity in the initial condition, rather than in the equation, can help in existence of irregular solutions (for example of class H ´1´ǫ in the vorticity), see Albeverio and Cruzeiro [1] and more recently Flandoli and Luo [45], Grotto and Romito [53] and Grotto, Luongo and Romito [52].…”

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confidence: 99%

Regularized vortex approximation for 2D Euler equations with transport noise

Coghi

Maurelli

2020

Stoch. Dyn.

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We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot–Savart kernel and the same common noise. The approximation happens by sending the number of particles [Formula: see text] to infinity and the regularization [Formula: see text] in the Biot–Savart kernel to [Formula: see text], as a suitable function of [Formula: see text].

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Hydrodynamic Models

Ferrario

Flandoli²

2023

Springer Proceedings in Mathematics &Amp; Statistics

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$$\rho $$ ρ -White noise solution to 2D stochastic Euler equations

Cited by 17 publications

References 24 publications

Well-posedness for a stochastic 2D Euler equation with transport noise

Well-posedness for a stochastic 2D Euler equation with transport noise

Regularized vortex approximation for 2D Euler equations with transport noise

Hydrodynamic Models

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