Local Martingale and Pathwise Solutions for an Abstract Fluids Model

Abstract

We establish the existence and uniqueness of both local martingale and local pathwise solutions of an abstract nonlinear stochastic evolution system. The primary application of this abstract framework is to infer the local existence of strong, pathwise solutions to the 3D primitive equations of the oceans and atmosphere forced by a nonlinear multiplicative white noise. Instead of developing our results specifically for the 3D primitive equations we choose to develop them in a slightly abstract framework which covers many related forms of these equations (atmosphere, oceans, coupled atmosphere-ocean, on the sphere, on the β-plane approximation etc and the incompressible Navier-Stokes equations). In applications, all of the details are given for the β-plane approximation of the oceans equations.

References in corpus (2)

• Global L_2-solutions of stochastic Navier-Stokes equations
• Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise

Cited by in corpus (33)

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• On the small time asymptotics of 3D stochastic primitive equations
• Global well-posedness of the viscous Camassa--Holm equation with gradient noise
• On a stochastic Camassa-Holm type equation with higher order nonlinearities
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• Existence and large time behaviour for a stochastic model of a modified magnetohydrodynamic equations
• Ergodicity in Randomly Forced Rayleigh-Bénard Convection
• Homogenization of nonlinear stochastic partial differential equations in a general ergodic environment
• Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
• Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities
• Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise
• Dissipative solutions to the stochastic Euler equations
• No blow-up by nonlinear Itô noise for the Euler equations
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• The primitive equations with stochastic wind driven boundary conditions
• Stochastic Navier-Stokes equations for compressible fluids
• Well-Posedness of the 3D Stochastic Primitive Equations with Transport Noise
• Invariant measures for a class of stochastic third grade fluid equations in $2D$ and $3D$ bounded domains
• Solution theory of fractional SDEs in complete subcritical regimes
• Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport
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• On weak-strong uniqueness and singular limit for the compressible Primitive Equations
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