论文标题
带有随机初始数据的Cahn-Hilliard-Navier-Stokes方程的适应性良好
Well-posedness for the Cahn-Hilliard-Navier-Stokes equation with random initial data
论文作者
论文摘要
在本文中，我们将Cauchy问题的几乎确定的稳定性与Cahn-Hilliard-Navier-Stokes方程式相关，并在圆环$ \ Mathbb {t}^3 $上具有随机的初始数据。首先，我们证明了解决方案的局部存在和独特性。此外，我们证明了解决方案的全球存在和独特性，并在小初始数据的条件下给出了相对概率估计。
In this paper, we consider the almost sure well-posedness of the Cauchy problem to the Cahn-Hilliard-Navier-Stokes equation with a randomization initial data on a torus $\mathbb{T}^3$. First, we prove the local existence and uniqueness of solution. Furthermore, we prove the global existence and uniqueness of solution and give the relative probability estimate under the condition of small initial data.
