Invariant measure for 2D stochastic Cahn–Hilliard–Navier–Stokes equations,Stochastics and Dynamics

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Invariant measure for 2D stochastic Cahn–Hilliard–Navier–Stokes equations
Stochastics and Dynamics ( IF 1.1 ) Pub Date : 2023-06-20 , DOI: 10.1142/s0219493723500302
Zhaoyang Qiu _{1,

2,

3} , Huaqiao Wang _{1,

2,

3} , Daiwen Huang _{1,

2,

3}

Affiliation

In this paper, we investigate the stochastic Cahn–Hilliard–Navier–Stokes equations in two-dimensional spaces. Applying the Maslowski–Seidler method, we establish the existence of invariant measure in state space $L_{x}^{2} \times H^{1}$ with the weak topology. We also prove the existence of global pathwise solutions using the stochastic compactness argument.

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