Axisymmetric Solutions to Coupled Navier-Stokes/Allen-Cahn Equations
Axisymmetric Solutions to Coupled Navier-Stokes/Allen-Cahn Equations
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DOI：
10.1137/090754698
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发表时间：
2010-01
期刊：
影响因子：
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通讯作者：
Xiang Xu;Liyun Zhao;Chun Liu
中科院分区：
文献类型：
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作者：
Xiang Xu;Liyun Zhao;Chun Liu
本文研究了$\mathbb{R}^3$中Navier-Stokes方程和Allen-Cahn方程耦合的一类轴对称解。首先，从分离变量法导出一维方程组，该方程组沿着其对称轴逼近三维系统。在此基础上，通过加入扰动项，构造了三维系统的有限能量解。我们证明了在大粘性和小初始数据的情况下构造的解的全局正则性。这些解可以看作是无限能量解附近的扰动。
We investigate a family of axisymmetric solutions to a coupling of Navier–Stokes and Allen–Cahn equations in $\mathbb{R}^3$. First, a one-dimensional system of equations is derived from the method of separation of variables, which approximates the three-dimensional system along its symmetry axis. Then based on them, by adding perturbation terms, we construct finite energy solutions to the three-dimensional system. We prove the global regularity of the constructed solutions in both large viscosity and small initial data cases. These solutions can be considered as perturbations near infinite-energy solutions.