Nonlinear Schrödinger equations in the Sobolev space of critical order (Q1266267)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Nonlinear Schrödinger equations in the Sobolev space of critical order |
scientific article; zbMATH DE number 1199815
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear Schrödinger equations in the Sobolev space of critical order |
scientific article; zbMATH DE number 1199815 |
Statements
Nonlinear Schrödinger equations in the Sobolev space of critical order (English)
0 references
8 April 1999
0 references
The nonlinear Schrödinger equation \(i\partial_t u+\Delta u= f(u)\) is considered. The main result of this paper states the global well-posedness in \(H^{n/2}\) for small Cauchy data. In particular, the case \(f(u)= \lambda| u|^{p-1}u\) is investigated.
0 references
global well-posedness
0 references
small Cauchy data
0 references
0 references
0 references
0 references
0 references
0 references
