Well-posedness for the Cahn-Hilliard-Navier-Stokes equation with random initial data

Zhaoyang Qiu; Huaqiao Wang

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arXiv · 2002.05043

Well-posedness for the Cahn-Hilliard-Navier-Stokes equation with random initial data

Zhaoyang Qiu·Huaqiao Wang

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Abstract

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.

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Zhaoyang Qiu, Huaqiao Wang. 2020-02-12. Well-posedness for the Cahn-Hilliard-Navier-Stokes equation with random initial data. https://arxiv.org/abs/2002.05043

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