Lower Bounds of Possible Blow-Up Solutions of the Electron Magnetohydrodynamics Equations

IF 1 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2026-06-05 Epub Date: 2026-04-11 DOI:10.1002/mana.70146

Yulin Ye, Yanqing Wang

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引用次数: 0

Abstract

In this paper, we investigate the blow-up rates of strong solutions to the electron magnetohydrodynamics (EMHD) equations. The optimal lower bounds of potential blow-up solutions of the EMHD equations in homogeneous Sobolev spaces ${\dot{H}}^{s} (R^{n})$ are shown, where $n / 2 < s < (n + 2) / 2$ for spatial dimensions $n = 2, 3$ . Moreover, for $s \geq (n + 2) / 2$ , the blow-up rates of solutions in this system in spaces ${\dot{H}}^{s} (R^{n})$ are also obtained. The proof relies on the cancellation of the Hall term and Kato–Ponce commutator estimate in the homogeneous setting.

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电子磁流体动力学方程可能爆破解的下界

本文研究了电子磁流体动力学（EMHD）方程强解的爆破率。齐次Sobolev空间中EMHD方程势爆破解的最优下界H （s (R) n）$\dot{H}^{s}(\mathbb {R}^{n})$显示，其中n / 2 ＆lt； s ＆lt; (n + 2) / 2 $n/2<s<(n+2)/2$对于空间维度n = 2，3 . $n=2, 3$。当s≥(n + 2) / 2 $ s\ge (n+2)/2$时，得到了该体系溶液在H (s (R) n) $\dot{H}^{s}(\mathbb {R}^{n})$空间中的爆破率。该证明依赖于齐次条件下Hall项和Kato-Ponce换向子估计的消去。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index