具有密度依赖粘度和自由边界的一维可压缩Navier-Stokes/Allen-Cahn系统的全局解

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2023-11-29 DOI:10.1007/s10473-024-0111-5

Shijin Ding, Yinghua Li, Yu Wang

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引用次数: 0

摘要

本文研究了用于模拟非混相两相流动力学的Navier-Stokes/Allen-Cahn系统。我们考虑一维自由边界问题，并假设粘度系数以η(ρ) = ρα的形式依赖于密度。当\(0 < \alpha < {1 \over 4}\)时，证明了自由边界问题h - m-解(m∈＿1)的存在性。进一步，我们得到了初始数据光滑时的全局C∞解。

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Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary

This paper is concerned with the Navier-Stokes/Allen-Cahn system, which is used to model the dynamics of immiscible two-phase flows. We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form of η(ρ) = ρ^α. The existence of unique global H^2m-solutions (m ∈ ℕ) to the free boundary problem is proven for when \(0 < \alpha < {1 \over 4}\). Furthermore, we obtain the global C^∞-solutions if the initial data is smooth.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.