The Cauchy problem for critical and subcritical semilinear parabolic equations in \(L^r\). II: Initial data in critical Sobolev spaces \(\dot{H}^{-s,r^s}\)
type: Item
instance of: scholarly article
title: The Cauchy problem for critical and subcritical semilinear parabolic equations in \(L^r\). II: Initial data in critical Sobolev spaces \(\dot{H}^{-s,r^s}\)
zbMATH Open document ID: 1032.35086
DOI: 10.1016/S0362-546X(02)00136-0
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The paper deals with the Cauchy problem in critical Sobolev spaces of negative indices for semilinear parabolic equations. Local and global existence and uniqueness is established by means of time-space \(L^p\)-\(L^r\) estimates. The complex (derivative) Ginzburg-Landau and the Cahn-Hilliard equations are special cases of these studied at the paper.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1879983
zbMATH Keywords: complex Ginzburg-landau equation
zbMATH Keywords: Cahn-Hilliard equations
zbMATH Keywords: time-space \(L^p\)-\(L^r\) estimate
zbMATH Keywords: critical Sobolev spaces of negative indices
zbMATH Keywords: rough initial data
author: Baoxiang Wang
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00136-0
OpenAlex ID: W1966644877
description: scientific article; zbMATH DE number 1879983