无粘轴对称MHD-Boussinesq系统的大数据全局适定性

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2023-10-03 DOI:10.1007/s10440-023-00608-z

Zijin Li, Zhaojun Xing, Meixian Yang

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引用次数: 0

摘要

给出了Sobolev空间\(H^{m}\)中具有大轴对称初始数据的三维无粘MHD-Boussinesq系统的全局适定性。为了克服在时间均匀\(H^{1}\)估计中出现的困难，发现了一个重新表述的良好未知数系统，并给出了一个中间估计。在此基础上，验证了无粘MHD-Boussinesq系统的beale - kato - majda型判据。然后利用经典能量法和换向子的估计得到了高阶估计。最后，我们证明了全局实时解的\(H^{m}\)范数在时间上的增长速度并不快于四倍指数函数\((\forall m\in \mathbb{N})\)。

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On the Large Data Global Well-Posedness of Inviscid Axially Symmetric MHD-Boussinesq System

The global well-posedness of the 3D inviscid MHD-Boussinesq system, with large axisymmetric initial data, in the Sobolev space \(H^{m}\) is given. To overcome difficulties that arise in the time-uniform \(H^{1}\) estimate, a reformulated system of good unknowns is discovered and an intermediate estimate is shown. Based on the reformulated system, a Beale-Kato-Majda-type criterion of the inviscid MHD-Boussinesq system is verified. Then higher-order estimates are concluded by the classical energy method and estimates of commutators. At last, we show the \(H^{m}\) norm of the global-in-time solution temporally grows no faster than a four times exponential function \((\forall m\in \mathbb{N})\).

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.