2023
DOI: 10.48550/arxiv.2301.07810
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Pathwise Solutions for Stochastic Hydrostatic Euler Equations and Hydrostatic Navier-Stokes Equations Under the Local Rayleigh Condition

Abstract: Stochastic factors are not negligible in applications of hydrostatic Euler equations (EE) and hydrostatic Navier-Stokes equations (NSE). Compared with the deterministic cases for which the illposedness of these models in the Sobolev spaces can be overcome by imposing the local Rayleigh condition on the initial data, the studies on the well-posedness of stochastic models are still limited.In this paper, we consider the initial data to be a random variable in a certain Sobolev space and satisfy the local Rayleig… Show more

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“…See also [25] for the stochastic fractional Boussinesq equations. For the recent progress for other stochastic fluid euations, see, for example, [11,13,21] for the stochastic Euler equations and [12,15,16,23,24] for the stochastic primitive equations.…”
Section: Introductionmentioning
confidence: 99%
“…See also [25] for the stochastic fractional Boussinesq equations. For the recent progress for other stochastic fluid euations, see, for example, [11,13,21] for the stochastic Euler equations and [12,15,16,23,24] for the stochastic primitive equations.…”
Section: Introductionmentioning
confidence: 99%