Regularity of solutions to nonlinear dispersive equations
type: Item
instance of: scholarly article
title: Regularity of solutions to nonlinear dispersive equations
zbMATH Open document ID: 0699.35036
DOI: 10.1016/0022-0396(89)90078-8
author: G. Ponce
published in: Journal of Differential Equations
publication date: 1989-01-01T00:00:00Z
review text: The author studies the regularity of solutions of nonlinear dispersive equations under decay assumptions on the derivatives of the data. Thus he obtains conditions guaranteeing this solution to have the same regularity as that of the associated linear problem. Finally, the author remarks that by \textit{S. Klainerman} [Commun. Pure Appl. Math. 38, 321-332 (1985; Zbl 0635.35059)] a similar principle (the commutative properties of the D'Alembertian operator and the Lorentz group) was successfully used to show the existence of a global small solution to nonlinear wave equations.
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4146510
zbMATH Keywords: generalized Korteweg-de Vries equation
zbMATH Keywords: nonlinear Schrödinger
zbMATH Keywords: equation
zbMATH Keywords: regularity
zbMATH Keywords: nonlinear dispersive equations
zbMATH Keywords: decay assumptions
reviewed by: Hiroshi Haruki
MaRDI profile type: Publication
full work available at URL: 0022-0396(89)90078-8
OpenAlex ID: W1964379900
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description: scientific article; zbMATH DE number 4146510