The Global Well-posedness for the 2D Leray-α MHD Equations with Zero Magnetic Diffusivity

By means of Fourier frequency localization and Bony＇s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the α model, then using the ene...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 32; no. 10; pp. 1145 - 1158
Main Author Chen, Qiong Lei
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.10.2016
Subjects
Diffusivity
Estimates
Fourier analysis
Inequalities
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
MHD方程
Texts
Two dimensional
二维
对数Sobolev不等式
扩散率
整体存在性
水动力学模型
能量估计
适定性
35B65
Littlewood–Paley decomposition
MHD equations
blow-up criterion
76W05
Leray
Online AccessGet full text
ISSN1439-8516
1439-7617
DOI10.1007/s10114-016-5521-4

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Summary:By means of Fourier frequency localization and Bony＇s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the α model, then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality, we obtain the estimate ∫0^t ｜｜△u｜｜L∞ds which is crucial to get the global existence for the general initial data.
Bibliography:By means of Fourier frequency localization and Bony＇s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the α model, then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality, we obtain the estimate ∫0^t ｜｜△u｜｜L∞ds which is crucial to get the global existence for the general initial data.
Leray-a-MHD equations, blow-up criterion, Littlewood-Paley decomposition
11-2039/O1
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-5521-4