Global well‐posedness for two modified‐Leray‐α‐MHD models with partial viscous terms

In this paper, we will prove global well‐posedness for the Cauchy problems of two modified‐Leray‐α‐MHD models with partial viscous terms. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Yong Zhou,et al.  Regularity criteria for the solutions to the 3D MHD equations in the multiplier space , 2010 .

[2]  Jiahong Wu,et al.  Regularity Criteria for the Generalized MHD Equations , 2008 .

[3]  Yong Zhou,et al.  Regularity criteria for the generalized viscous MHD equations , 2007 .

[4]  Zhifei Zhang,et al.  The Beale-Kato-Majda Criterion for the 3D Magneto-Hydrodynamics Equations , 2007, math/0701054.

[5]  E. Titi,et al.  Analytical study of certain magnetohydrodynamic-α models , 2006, math/0606603.

[6]  Yong Zhou,et al.  Regularity criteria for the 3D MHD equations in terms of the pressure , 2006 .

[7]  E. Titi,et al.  Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models , 2006, physics/0608096.

[8]  Alexei Ilyin,et al.  A modified-Leray-α subgrid scale model of turbulence , 2006 .

[9]  Zhouping Xin,et al.  On the regularity of weak solutions to the magnetohydrodynamic equations , 2005 .

[10]  Yong Zhou,et al.  Remarks on regularities for the 3D MHD equations , 2005 .

[11]  Y. Meyer,et al.  Compensated compactness and Hardy spaces , 1993 .

[12]  T. Ozawa On critical cases of Sobolev inequalities , 1992 .

[13]  Luis Vega,et al.  Well-posedness of the initial value problem for the Korteweg-de Vries equation , 1991 .

[14]  Tosio Kato,et al.  Commutator estimates and the euler and navier‐stokes equations , 1988 .

[15]  Roger Temam,et al.  Some mathematical questions related to the MHD equations , 1983 .

[16]  Haim Brezis,et al.  A note on limiting cases of sobolev embeddings and convolution inequalities , 1980 .

[17]  Thierry Gallouët,et al.  Nonlinear Schrödinger evolution equations , 1980 .