Lévy噪声驱使的随机二维Cahn-Hilliard-Navier-Stokes方程解的存在唯一性

On the Existence and Uniqueness of Solution to a Stochastic 2D Cahn-Hilliard-Navier-Stokes Model Driven by Lévy Noise

研究Lévy过程驱使的随机二维有界域中耦合的Cahn-Hilliard-Navier-Stokes方程,该方程是控制速度的Navier-Stokes方程和控制相参数的Cahn-Hilliard模型的耦合.讨论其系数在Lipschitz条件下方程解的适定性问题.通过Young不等式、It?公式和Gronwall引理,利用一致估计、弱收敛以及Galerkin方法,证明在Lévy噪声驱使下,随机二维方程解的存在性和唯一性.

This paper studies the coupled Cahn-Hilliard-Navier-Stokes equations in the stochastic two-dimensional bounded domain driven by the Lévy process,which is the coupling of the NavierStokes equations controlling the velocity and the Cahn-Hilliard model controlling the phase parameters.This paper discusses the problem of the well-posedness of the solution under the Lipschitz condition.Through the Young’s inequality,It?formula,Gronwall lemma,using the consistent estimation,weak convergence and Galerkin method,it aims to prove the existence and uniqueness of the solution of the stochastic two-dimensional equation driven by Lévy noise.