Abstract A well-known diffuse interface model consists of the Navier-Stokes equations for the average velocity, nonlinearly coupled with a convective Cahn-Hilliard type equation for the order (phase) parameter. This system describes the evolution of an incompressible isothermal mixture of binary fluids and it has been investigated by many authors. Here we consider a stochastic version of this model forced by a multiplicative white noise on a bounded domain of R d , d = 2 , 3 . We prove the existence and uniqueness of a local maximal strong solution when the initial data ( u 0 , ϕ 0 ) takes values in H 1 × H 2 . Moreover in the two-dimensional case, we prove that our solution is global.

中文翻译：

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随机 Cahn-Hilliard-Navier-Stokes 系统的强解

摘要 众所周知的扩散界面模型由平均速度的 Navier-Stokes 方程组成，非线性耦合与阶（相位）参数的对流 Cahn-Hilliard 型方程。该系统描述了不可压缩的二元流体等温混合物的演化，许多作者对此进行了研究。在这里，我们考虑该模型的随机版本，由 R d , d = 2 , 3 的有界域上的乘法白噪声强制。我们证明了当初始数据 (u 0 , ϕ 0 ) 取值为 H 1 × H 2 时局部极大强解的存在性和唯一性。此外，在二维情况下，我们证明了我们的解决方案是全局的。