广义MHD方程的全局适定性和大时态

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-04-28 DOI:10.1016/j.nonrwa.2025.104384

Huan Yu , Haifeng Shang

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引用次数: 0

摘要

本文研究了nD广义MHD方程。通过使用一种新的方法，不同于Schonbek （Schonbek, 1985, 1986）和谱表示技术（Kajikiya和Miyakawa， 1986）开发的经典傅里叶分裂方法，我们恢复并改进了一些已知的弱解的衰减结果。此外，通过将非线性项改写为新的换向子来有效地分配导数，我们得到了具有小耗散指数β的nD广义MHD方程整体解的存在唯一性和最优衰减估计。

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Global well-posedness and large time behaviors for the generalized MHD equations

In this paper, we are concerned with the

n

D generalized MHD equations. By using a new approach, different from the classical Fourier splitting method developed by Schonbek (Schonbek, 1985, 1986) and the spectral representation technique (Kajikiya and Miyakawa, 1986), we recover and improve some known decay results of weak solutions. Besides, by rewriting the nonlinear terms into new commutators to efficiently distribute derivatives, we obtain the existence, uniqueness and optimal decay estimates of global solutions for the

n

D generalized MHD equations with small dissipation index

β

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.