THE GLOBAL L2 STABILITY OF SOLUTIONS TO THREE DIMENSIONAL MHD EQUATIONS
查看参考文献25篇
文摘
|
In this paper, we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded, domains. Under suitable conditions of the large solutions, it is shown that the large solutions are stable. And we obtain the equivalent condition of this stability condition. Moreover, the global existence and the stability of two-dimensional MHD equations under three-dimensional perturbations are also established. |
来源
|
Acta Mathematica Scientia
,2013,33(1):247-267 【核心库】
|
DOI
|
10.1016/s0252-9602(12)60208-2
|
关键词
|
MHD equations
;
strong solutions
;
stability
|
地址
|
1.
Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190
2.
Department of Mathematics, Beijing Technology and Business University, Beijing, 100048
|
语种
|
英文 |
文献类型
|
研究性论文 |
ISSN
|
0252-9602 |
学科
|
数学 |
基金
|
This work is supported by 973 Program
;
国家自然科学基金
|
文献收藏号
|
CSCD:4770499
|
参考文献 共
25
共2页
|
1.
Schonbek M E. Lower bounds of rates of decay for solutions to Navier-Stokes equations.
I Amer Math Soc,1991,4(3):423-449
|
被引
15
次
|
|
|
|
2.
Schonbek M E. Asymptotic behavior of solutions to the three-dimensional Navier-Stokes equations.
Indiana Univ Math J,1992,41(3):809-823
|
被引
5
次
|
|
|
|
3.
He C. Weighted energy inequalities for nonstationary Navier-Stokes equations.
J Diff Eqns,1998,148:422-444
|
被引
4
次
|
|
|
|
4.
He C. On the regularity of weak solutions to the magnetohydrodynamic equations.
J Diff Equas,2005,213:235-254
|
被引
57
次
|
|
|
|
5.
Ponce G. Global stability of large solutions to the 3D Navier-Stokes equations.
Commun Math Phys,1994,159:329-341
|
被引
7
次
|
|
|
|
6.
He C. On the decay properties of solutions to the non-stationary Navier-Stokes equations in R3.
Proc Roy Soc Edinburgh Sect A,2001,131:597-619
|
被引
11
次
|
|
|
|
7.
He C. Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations.
J Funct Anal,2005,227:113-152
|
被引
22
次
|
|
|
|
8.
Jiu Q. Remarks on the regularity to 3-D ideal Magnetohydynamic equations.
Acta Math Sinica,2004,20(4):695-708
|
被引
3
次
|
|
|
|
9.
Heywood J G. The Navier-Stokes equations: On the existence, regularity and decay of solutions.
Indiana Univ Math J,1980,29:639-681
|
被引
12
次
|
|
|
|
10.
Stein E M.
Singular Integrals and Differentiality Properties of Functions,1970
|
被引
3
次
|
|
|
|
11.
Schonbek M. The long time behavior of solutions to MHD equations.
Math Annalen,1996,304:717-756
|
被引
15
次
|
|
|
|
12.
Ladyzhenskaya O A.
The Mathematical Theory of Viscous Incompressible Flow,1969
|
被引
27
次
|
|
|
|
13.
Kajikiya R. On L2 decay of weak solutions of the Navier-Stokes equations in Rn.
Math Z,1986,192:135-148
|
被引
9
次
|
|
|
|
14.
Miyakawa T. On optimal decay rates for solutions to the Navier-Stokes equations in Rn.
Proceedings of Partial Equations and Applications. Math Bohem,2001,126(2):443-455
|
被引
1
次
|
|
|
|
15.
Zhao C. On Global L2 stability of large solutions to the three-dimensional evolution system of MHD type describing geophysical flow.
Acta Mathematica Sinica, Chinese Series,2001,44(6):961-976
|
被引
3
次
|
|
|
|
16.
He C. ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS.
Acta Mathematica Scientia. B,2009,29(3):583-598
|
被引
2
次
|
|
|
|
17.
Li X. The global L2 stability of large solutions to three dimensional Boussinesq equations.
Acta Mathematic Sinica,2010,53(1):171-186
|
被引
1
次
|
|
|
|
18.
Liu Y. L2 Decay for weak solutions of the MHD equations in half space.
Acta Mathematica Scientia. B,2010,30(4):1166-1175
|
被引
1
次
|
|
|
|
19.
Jiu Q. Mathematical results related to a two dimensional magneto-hydrodynamic equations.
Acta Mathematica Scientia. B,2006,26(4):744-756
|
被引
4
次
|
|
|
|
20.
Liu X. New regularity conditions for magneto-hydrodynamics equations.
Acta Mathematica Scientia. A,2010,30(2):335-343
|
被引
1
次
|
|
|
|
|