密度和导电率可变的不可压缩多流体力学方程的全局唯一解

IF 1.2 4区数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0507-2

Xueli Ke

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引用次数: 0

摘要

我们研究了二维非均质不可压缩 MHD 方程的全局唯一解，初始数据 (u0, B0) 位于临界贝索夫空间 \(\dot{B}_{p,1}^{{-1}+{{2}\over{p}}}(\mathbb{R}^{2})\) (1 < p < 2)，初始密度 ρ0 接近正常数。通过使用加权全局估计、斯托克斯系统洛伦兹空间中的最大正则估计以及拉格朗日方法，我们证明了二维 MHD 方程具有唯一的全局解。

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Global unique solutions for the incompressible MHD equations with variable density and electrical conductivity

We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data (u₀, B₀) being located in the critical Besov space \(\dot{B}_{p,1}^{{-1}+{{2}\over{p}}}(\mathbb{R}^{2})\) (1 < p < 2) and the initial density ρ₀ being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.

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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.