Geodesic
Global well-posedness for KdV in Sobolev spaces of negative index
Electronic journal of differential equations, Tome 2001 (2001)
The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in $H^s(\mathbb{R})$ for -3/10 s.
Classification : 35Q53, 42B35, 37K10
Keywords: Korteweg-de Vries equation, nonlinear dispersive equations, bilinear estimates 
@article{EJDE_2001__2001__a24,
     author = {Colliander,  James E. and Keel,  Markus and Staffilani,  Gigliola and Takaoka,  Hideo and Tao,  Terence C.},
     title = {Global well-posedness for {KdV} in {Sobolev} spaces of negative index},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0967.35119},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a24/}
}
TY  - JOUR
AU  - Colliander,  James E.
AU  - Keel,  Markus
AU  - Staffilani,  Gigliola
AU  - Takaoka,  Hideo
AU  - Tao,  Terence C.
TI  - Global well-posedness for KdV in Sobolev spaces of negative index
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a24/
LA  - en
ID  - EJDE_2001__2001__a24
ER  - 
%0 Journal Article
%A Colliander,  James E.
%A Keel,  Markus
%A Staffilani,  Gigliola
%A Takaoka,  Hideo
%A Tao,  Terence C.
%T Global well-posedness for KdV in Sobolev spaces of negative index
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a24/
%G en
%F EJDE_2001__2001__a24
Colliander,  James E.; Keel,  Markus; Staffilani,  Gigliola; Takaoka,  Hideo; Tao,  Terence C. Global well-posedness for KdV in Sobolev spaces of negative index. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a24/