DC Field | Value | Language |
---|---|---|
dc.contributor.author | Guo, Zihua | ko |
dc.contributor.author | Kwak, Chulkwang | ko |
dc.contributor.author | Kwon, Soonsik | ko |
dc.date.accessioned | 2019-04-15T14:50:41Z | - |
dc.date.available | 2019-04-15T14:50:41Z | - |
dc.date.created | 2013-10-14 | - |
dc.date.issued | 2013-12 | - |
dc.identifier.citation | JOURNAL OF FUNCTIONAL ANALYSIS, v.265, no.11, pp.2791 - 2829 | - |
dc.identifier.issn | 0022-1236 | - |
dc.identifier.uri | http://hdl.handle.net/10203/254425 | - |
dc.description.abstract | We consider the Cauchy problem of the fifth-order equation arising from the Korteweg-de Vries (KdV) hierarchy {partial derivative(t)u + partial derivative(5)(x)u + c(1)partial derivative(x)u partial derivative(2)(x)u + c(2)u partial derivative(3)(x)u = 0, x, t is an element of R, u(0, x) = u(0)(x), u(0) is an element of H-s(R). We prove a priori bound of solutions for H-s (R) with s >= 5/4 and the local well-posedness for s >= 2. The method is a short time X-s,X-b space, which was first developed by Ionescu, Kenig and Tataru [13] in the context of the KP-I equation. In addition, we use a weight on localized Xs,b structures to reduce the contribution of high low frequency interaction where the low frequency has large modulation. As an immediate result from a conservation law, we obtain that the fifth-order equation in the KdV hierarchy, partial derivative(t)u - partial derivative(5)(x)u - 30u(2)partial derivative(x)u + 20 partial derivative(x)u partial derivative(2)(x)u + 10u partial derivative(3)(x)u = 0 is globally well-posed in the energy space H-2. (C) 2013 Elsevier Inc. All rights reserved. | - |
dc.language | English | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.subject | GLOBAL WELL-POSEDNESS | - |
dc.subject | NONLINEAR DISPERSIVE EQUATIONS | - |
dc.subject | BENJAMIN-ONO-EQUATION | - |
dc.subject | DE-VRIES EQUATION | - |
dc.subject | A-PRIORI BOUNDS | - |
dc.subject | BURGERS EQUATION | - |
dc.subject | SOBOLEV SPACES | - |
dc.subject | INVISCID LIMIT | - |
dc.subject | ORDER | - |
dc.title | Rough solutions of the fifth-order KdV equations | - |
dc.type | Article | - |
dc.identifier.wosid | 000324603100006 | - |
dc.identifier.scopusid | 2-s2.0-84883820205 | - |
dc.type.rims | ART | - |
dc.citation.volume | 265 | - |
dc.citation.issue | 11 | - |
dc.citation.beginningpage | 2791 | - |
dc.citation.endingpage | 2829 | - |
dc.citation.publicationname | JOURNAL OF FUNCTIONAL ANALYSIS | - |
dc.identifier.doi | 10.1016/j.jfa.2013.08.010 | - |
dc.contributor.localauthor | Kwon, Soonsik | - |
dc.contributor.nonIdAuthor | Guo, Zihua | - |
dc.contributor.nonIdAuthor | Kwak, Chulkwang | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Local well-posedness | - |
dc.subject.keywordAuthor | Fifth-order KdV equation | - |
dc.subject.keywordAuthor | KdV hierarchy | - |
dc.subject.keywordAuthor | X-s,X-b space | - |
dc.subject.keywordPlus | GLOBAL WELL-POSEDNESS | - |
dc.subject.keywordPlus | NONLINEAR DISPERSIVE EQUATIONS | - |
dc.subject.keywordPlus | BENJAMIN-ONO-EQUATION | - |
dc.subject.keywordPlus | DE-VRIES EQUATION | - |
dc.subject.keywordPlus | A-PRIORI BOUNDS | - |
dc.subject.keywordPlus | BURGERS EQUATION | - |
dc.subject.keywordPlus | SOBOLEV SPACES | - |
dc.subject.keywordPlus | INVISCID LIMIT | - |
dc.subject.keywordPlus | ORDER | - |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.