广义磁流体方程组弱解的正则准则

李凤萍

(河南理工大学数学与信息科学学院,河南 焦作 454000)

广义磁流体方程组弱解的正则准则

李凤萍

(河南理工大学数学与信息科学学院,河南 焦作 454000)

利用能量估计法和Littlewood-Paley分解技术研究三维广义磁流体方程组轴对称弱解的正则性,并得到用速度场和磁场的旋度的方位角分量控制的正则准则.

广义磁流体方程组;轴对称弱解;正则准则

1 引言

2 预备知识

3 主要结论的证明

参考文献

[1]Cannone M,M iao C X,Prioux N,et al.The cauchy problem for the magneto-hydrodynam ic system[J]. Banach Center Publ.2006,74:59-93.

[2]Chen Q L,M iao C X,Zhang Z F.The Beale-Kato-M a jda criterion for the 3D m agneto-hydrodynam ics equations[J].Comm.M ath.Phys.,2007,275:861-872.

[3]He C,Wang Y.On the regu larity criteria for weak solutions to them agnetohydrodynam ic equations[J].J. D iff erential Equations,2007,238:1-17.

[4]He C,X in Z P.On the regularity ofweak solutions to them agnetohyd rodynam ic equations[J].J.Diff erential Equations,2005,213:235-254.

[5]Yuan B Q.B low-up criterion of sm ooth solutions to the MHD equations in Besov spaces[J].J.Syst.Sci. Com p lex,2005,18:277-284.

[6]Yuan B Q.On the blow-up criterion of sm ooth solutions to the MHD system in BMO space[J].Acta.M ath. App l.Sinica(English Series),2006,22:413-418.

[7]Zhou Y,Gala S.A new regu larity criterion for weak solutions to the viscous MHD equations in term s of the vorticity field[J].Nonlinear Anal.,2010,72:3643-3648.

[8]李凤萍,原保全.广义磁流体方程组轴对称弱解的正则准则[J].高校应用数学学报,2010,25(3):319-325.

[9]李凤萍.广义磁流体方程光滑解的爆破准则[J].山东大学学报:理学版,2010,45(3):90-94.

[10]Luo Y W.On the regularity of generalized MHD equations[J].J.M ath.Anal.App l.,2010,365:806-808.

[11]W u G.Regularity criteria for the 3D generalized MHD equations in term s of vorticity[J].Nonlinear Anal., 2009,71:4251-4258.

[12]Wu J H.Regu larity criteria for the generalized MHD equations[J].Comm.Partial Diff erential Equations, 2008,33:285-306.

[13]Wu J H.Generalized MHD equations[J].J.Diff erential Equations,2003,195:284-312.

[14]Yuan J.Existence theorem and regu larity criteria for the generalized MHD equations[J].Non linear Anal. RealW orld App l.,2010,11(3):1640-1649.

[15]Zhou Y.Regularity criteria for the generalized viscous MHD equations[J].Ann.Inst.H.Poincare.Anal. Non.Lineaire,2007,24:491-505.

The regu larity criterion to the w eak solu tions of the generalized m agnetohyd rodynam ic equations

Li Fengping

(School of M athem atics and Inform atics,Henan Polytechnic University,Jiaozuo 454000,China)

In this paper,we study the regularity criterion of the axisymm etric weak solutions to the generalized magneto-hydrodynam ic equations in R3by means of energy method and Littlewood-Paley decom position,and obtain a criterion by the azimuthal com ponents of vorticities to velocity and m agnetic field.

generalized magnetohyd rodynam ic equations,axisymmetric weak solution,regu larity criterion

O175.2

A

1008-5513(2012)06-0735-09

2012-07-02.

数学天元基金(11126119);河南省科技创新人才计划(2009HASTIT 007);河南理工大学青年骨干教师资助计划(649177);河南省杰出青年计划(104100510015);河南理工大学青年基金(Q 2011-14A).

李凤萍(1980-),硕士,讲师,研究方向:应用偏微分方程.

2010 M SC:76W 05,35B65