Lorentz空间中三维MHD方程的正则性$L^{3，∞}$

数学研究通讯 Pub Date : 2023-01-01 DOI:10.4208/cmr.2021-0048

Xian-gao Liu, Yueli Liu, Zixuan Liu

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引用次数: 0

摘要

本文考虑了三维MHD方程的正则性，证明了当速度场v∈L∞(0,T;L x (R3))具有局部小条件R∣∣{x∈Br(x0): |v(x,t0)|> ε R−1∣∣≤ε且磁场B∈L∞(0,T;VMO−1(R3))时，解(v,B,p)是Hölder连续的。AMS学科分类:35Q35、76B03、76D03

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Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$

The regularity for 3-D MHD equations is considered in this paper, it is proved that the solutions (v,B,p) are Hölder continuous if the velocity field v∈L∞(0,T;L x (R 3)) with local small condition r ∣∣ { x∈Br(x0) : |v(x,t0)|> εr −1 ∣∣≤ ε and the magnetic field B∈L∞(0,T;VMO−1(R3)). AMS subject classifications: 35Q35, 76B03, 76D03

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数学研究通讯

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