Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
type: Item
instance of: scholarly article
title: Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
zbMATH Open document ID: 0928.35158
author: G. Ponce
author: L. Vega
author: C. E. Kenig
published in: Inventiones Mathematicae
publication date: 1999-11-02T00:00:00Z
review text: The authors treat smoothing and local existence theory of generalized nonlinear Schrödinger equations where nonlinearities up to first order derivatives are allowed, and where the linear part may be nonelliptic. Those equations may model e.g. problems in water wave theory. One of their main results concerns the removal of size restriction for the initial data (which have to lie in certain Sobolev spaces) of local solutions; these solutions inherit a local smoothing effect in space time. The method consists in introducing the space derivatives of wave function as new variables, writing the original equation as a system, and using results of earlier papers of the same authors. The system has the advantage that the crucial term vanishes for \(t=0\) if a solution of the original equation is inserted.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35A07
zbMATH DE Number: 1275721
zbMATH Keywords: smoothing
zbMATH Keywords: nonlinear Schrödinger equations
zbMATH Keywords: generalized nonlinear Schrödinger equations
zbMATH Keywords: local smoothing effect in space time
reviewed by: Horst Lange
MaRDI profile type: Publication
full work available at URL: s002220050272
OpenAlex ID: W2047689815
DOI: 10.1007/S002220050272
description: scientific article; zbMATH DE number 1275721