廣義磁流體方程組弱解的正則準則

李鳳萍

(河南理工大學數學與信息科學學院,河南 焦作 454000)

廣義磁流體方程組弱解的正則準則

李鳳萍

(河南理工大學數學與信息科學學院,河南 焦作 454000)

利用能量估計法和Littlewood-Paley分解技術研究三維廣義磁流體方程組軸對稱弱解的正則性,并得到用速度場和磁場的旋度的方位角分量控制的正則準則.

廣義磁流體方程組;軸對稱弱解;正則準則

1 引言

2 預備知識

3 主要結論的證明

參考文獻

[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]李鳳萍,原保全.廣義磁流體方程組軸對稱弱解的正則準則[J].高校應用數學學報,2010,25(3):319-325.

[9]李鳳萍.廣義磁流體方程光滑解的爆破準則[J].山東大學學報:理學版,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.

數學天元基金(11126119);河南省科技創新人才計劃(2009HASTIT 007);河南理工大學青年骨干教師資助計劃(649177);河南省杰出青年計劃(104100510015);河南理工大學青年基金(Q 2011-14A).

李鳳萍(1980-),碩士,講師,研究方向:應用偏微分方程.

2010 M SC:76W 05,35B65