Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations

Abstract

We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions. The invariant measure is supported on strong solutions, but is furthermore shown to have higher regularity properties.

References in corpus (2)

• Ergodicity of Two Dimensional Turbulence
• Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics

Cited by in corpus (20)

• Global in time stability and accuracy of IMEX-FEM data assimilation schemes for the Navier-Stokes equations
• On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
• Exponential mixing for a class of dissipative PDEs with bounded degenerate noise
• Continuous data assimilation for the magnetohydrodynamic equations in 2D using one component of the velocity and magnetic fields
• Global martingale and pathwise solutions and infinite regularity of invariant measures for a stochastic modified Swift-Hohenberg equation
• Well-Posedness of the 3D Stochastic Primitive Equations with Transport Noise
• The primitive equations with stochastic wind driven boundary conditions
• Exponential Mixing for 3D Stochastic Primitive Equations
• Gaussian invariant measures and stationary solutions of 2D Primitive Equations
• Exponential stability of 3D stochastic primitive equations driven by fractional noise
• Controllability and ergodicity of 3D primitive equations driven by a finite-dimensional force
• Upper semi-continuity of random attractors and existence of invariant measures for nonlocal stochastic Swift-Hohenberg equation with multiplicative noise
• The stochastic Landau--Lifshitz--Baryakhtar equation: Global solution and invariant measure
• Bayesian Estimations for Diagonalizable Bilinear SPDEs
• Dynamic of the three dimensional viscous primitive equations of large-scale atmosphere
• Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data
• Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation
• Parameter Recovery and Sensitivity Analysis for the 2D Navier-Stokes Equations Via Continuous Data Assimilation
• The asymptotic behavior of primitive equations with multiplicative noise
• Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere