理想磁流体力学的磁螺旋度、弱解和弛豫

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-10-08 DOI:10.1002/cpa.22168

Daniel Faraco, Sauli Lindberg, László Székelyhidi Jr.

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引用次数: 0

摘要

在弱解的背景下，我们重新讨论了磁流体力学中的磁螺旋度守恒和Woltjer-Taylor弛豫理论。我们为理想MHD系统引入了一个松弛系统，该系统以与等离子体湍流中的观测结果一致的方式，将流体动力学湍流的影响（如雷诺应力项的出现）与磁螺旋度守恒解耦。作为副产品，我们回答了该领域中的两个悬而未决的问题：我们展示了磁螺旋度守恒的L3可积性条件的尖锐性，并为理想MHD耗散能量和交叉螺旋度但具有（任意）恒定磁螺旋度提供了湍流有界解。

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Magnetic helicity, weak solutions and relaxation of ideal MHD

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Magnetic helicity, weak solutions and relaxation of ideal MHD

We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics (MHD) in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects of hydrodynamic turbulence such as the appearance of a Reynolds stress term from the magnetic helicity conservation in a manner consistent with observations in plasma turbulence. As by-products we answer two open questions in the field: We show the sharpness of the L³ integrability condition for magnetic helicity conservation and provide turbulent bounded solutions for ideal MHD dissipating energy and cross helicity but with (arbitrary) constant magnetic helicity.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.