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)
Zbl   EuDML
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 
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/
@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},
     year = {2001},
     volume = {2001},
     zbl = {0972.35140},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a202/}
}
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