On the blow-up behavior of a nonlinear parabolic equation with periodic boundary conditions

被引:2
作者
Cortissoz, Jean C. [1 ,2 ]
机构
[1] Univ Los Andes, Dept Matemat, Bogota, Colombia
[2] Inst Colombiano Ciencias, Rincon Del Mar, Sucre, Colombia
关键词
Nonlinear parabolic equations; Periodic boundary conditions; Blow-up; NAVIER-STOKES EQUATIONS; UNIQUENESS THEOREM; EXISTENCE; SYSTEM;
D O I
10.1007/s00013-011-0266-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Using ideas arising in the works of LeJan and Sznitman and Mattingly and Sinai on their study of the Navier-Stokes equations, we investigate the blow-up behavior of a nonlinear parabolic equation subject to periodic boundary conditions.
引用
收藏
页码:69 / 78
页数:10
相关论文
共 12 条
[1]  
ANGENENT S, 1991, J DIFFER GEOM, V33, P601
[2]   SOME ELEMENTARY ESTIMATES FOR THE NAVIER-STOKES SYSTEM [J].
Cortissoz, Jean .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (10) :3343-3353
[3]  
FRIEDMAN A, 1986, ARCH RATION MECH AN, V96, P55
[4]  
GAGE M, 1986, J DIFFER GEOM, V23, P69
[5]  
Hamilton RS., 1988, Contemp. Math, V71, P237, DOI [DOI 10.1090/CONM/071/954419, 10.1090/conm/071/954419]
[6]  
LeJan Y, 1997, PROBAB THEORY REL, V109, P343
[7]   An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations [J].
Mattingly, JC ;
Sinai, YG .
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 1999, 1 (04) :497-516
[8]  
PASSO RD, 1987, J DIFFER EQUATIONS, V69, P1, DOI 10.1016/0022-0396(87)90099-4
[9]  
Sinai YG, 2008, PURE APPL MATH Q, V4, P71
[10]   Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source [J].
Souplet, P .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 153 (02) :374-406