北京工业大学学报
北京工業大學學報
북경공업대학학보
JOURNAL OF BEIJING POLYTECHNIC UNIVERSITY
2015年
2期
299-307
,共9页
三维%不可压%轴对称%正则性
三維%不可壓%軸對稱%正則性
삼유%불가압%축대칭%정칙성
three dimensional%incompressible%axial symmetric%regularity
为了研究解的正则性,研究了带旋涡的轴对称三维不可压MHD方程组。考虑2类特殊的MHD方程组的光滑弱解：uθ=0、Br =Bz =0和Br =Bz =0,通过采用能量法、Sobolev嵌入法等,证明了如果速度场的径向方向分量ur 满足一定条件,则可得到这2类三维不可压的轴对称MHD方程组弱解的正则性。
為瞭研究解的正則性,研究瞭帶鏇渦的軸對稱三維不可壓MHD方程組。攷慮2類特殊的MHD方程組的光滑弱解：uθ=0、Br =Bz =0和Br =Bz =0,通過採用能量法、Sobolev嵌入法等,證明瞭如果速度場的徑嚮方嚮分量ur 滿足一定條件,則可得到這2類三維不可壓的軸對稱MHD方程組弱解的正則性。
위료연구해적정칙성,연구료대선와적축대칭삼유불가압MHD방정조。고필2류특수적MHD방정조적광활약해：uθ=0、Br =Bz =0화Br =Bz =0,통과채용능량법、Sobolev감입법등,증명료여과속도장적경향방향분량ur 만족일정조건,칙가득도저2류삼유불가압적축대칭MHD방정조약해적정칙성。
To study the regularity criteria of solutions, the three-dimensional axially symmetric incompressible magnetohydrodynamics ( MHD ) equations with swirl are presented. Two types of particular weak solutions to the three-dimensional axially symmetric incompressible MHD equations uθ =0, Br=Bz=0, and Br=Bz=0 are considered. By using the energy method and the embedding method, the regularity criteria for the two types of weak solutions to the three-dimensional axially symmetric incompressible MHD equations are obtained if the radial direction component ur satisfies some conditions.
