Markov Selection and $W$-strong Feller for 3D Stochastic Primitive Equations

Abstract

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.

References in corpus (5)

• Local and Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity
• Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise
• Existence and uniqueness of weak solutions to viscous primitive equations for certain class of discontinuous initial data
• Exponential Mixing for 3D Stochastic Primitive Equations
• Random attractor of the 3D viscous primitive equations driven by fractional noises

Cited by in corpus (6)

• On the small time asymptotics of 3D stochastic primitive equations
• Well-Posedness of the 3D Stochastic Primitive Equations with Transport Noise
• The primitive equations with stochastic wind driven boundary conditions
• Exponential stability of 3D stochastic primitive equations driven by fractional noise
• Asymptotic behavior of 3-D stochastic primitive equations of large-scale moist atmosphere with additive noise
• Ergodicity for a class of semilinear stochastic partial differential equations