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arXiv · 1910.07904

On the Cauchy problem of 3D incompressible Navier-Stokes-Cahn-Hilliard system

Xiaopeng Zhao
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Abstract

In this paper, we are concerned with the well-posedness and large time behavior of Cauchy problem for 3D incompressible Navier-Stokes-Cahn-Hilliard equations. First, using Banach fixed point theorem, we establish the local well-posedness of solutions. Second, assuming $\|(u_0,\nabla\phi_0)\|_{\dot{H}^\frac12}$ is sufficiently small, we obtain the global well-posedness of solutions. Moreover, the optimal decay rates of the higher-order spatial derivatives of the solution are also obtained.

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Xiaopeng Zhao. 2019-10-15. On the Cauchy problem of 3D incompressible Navier-Stokes-Cahn-Hilliard system. https://arxiv.org/abs/1910.07904

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