三维大振荡真空有界区域中全可压缩磁流体动力系统的全局适定性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-09-23 DOI:10.1016/j.nonrwa.2025.104507

Yazhou Chen , Yunkun Chen , Xue Wang

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引用次数: 0

摘要

在一般有界域中研究了三维全可压缩磁流体动力系统，速度场具有滑移边界条件，温度场具有绝热条件，磁场具有完全导通条件。对于能量小但可能振荡大的正则初始数据，得到了该系统初边值问题的经典解和弱解的整体存在性以及指数衰减率。特别地，这种经典溶液的密度和温度都被允许在初始时消失。此外，还表明，对于经典解，当初始真空出现时（即使在某一点），密度的振荡将以指数速率无界增长。为了克服由滑移边界条件引起的困难，提出了一些新的观测和有用的估计。

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Global well-posedness of full compressible magnetohydrodynamic system in 3D bounded domains with large oscillations and vacuum

The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the magnetic field. For the regular initial data with small energy but possibly large oscillations, the global existence of classical and weak solution as well as the exponential decay rate to the initial-boundary-value problem of this system is obtained. In particular, the density and temperature of such a classical solution are both allowed to vanish initially. Moreover, it is also shown that for the classical solutions, the oscillation of the density will grow unboundedly with an exponential rate when the initial vacuum appears (even at a point). Some new observations and useful estimates are developed to overcome the difficulties caused by the slip boundary conditions.

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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.