Geodesic
Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we study the existence of global solutions to Schrodinger equations in one space dimension with a derivative in a nonlinear term. For the Cauchy problem we assume that the data belongs to a Sobolev space weaker than the finite energy space $H^{1}$. Global existence for $H^{1}$ data follows from the local existence and the use of a conserved quantity. For $H^{s}$ data with s1, the main idea is to use a conservation law and a frequency decomposition of the Cauchy data then follow the method introduced by Bourgain [3]. Our proof relies on a generalization of the tri-linear estimates associated with the Fourier restriction norm method used in [1,25].
Classification : 35Q55
Keywords: nonlinear Schrödinger equation, well-posedness 
@article{EJDE_2001__2001__a202,
     author = {Takaoka, Hideo},
     title = {Global well-posedness for {Schr\"odinger} equations with derivative in a nonlinear term and data in low-order {Sobolev} spaces},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a202/}
}
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Takaoka, Hideo. Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a202/