Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 곽철광 | * |
dc.date.accessioned | 2020-08-20T16:30:12Z | - |
dc.date.available | 2020-08-20T16:30:12Z | - |
dc.date.issued | 2020 | * |
dc.identifier.issn | 0294-1449 | * |
dc.identifier.issn | 1873-1430 | * |
dc.identifier.other | OAK-27662 | * |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/254987 | - |
dc.description.abstract | This paper is concerned with the Cauchy problem of the modified Kawahara equation (posed on T), which is well-known as a model of capillary-gravity waves in an infinitely long canal over a flat bottom in a long wave regime [26]. We show in this paper some well-posedness results, mainly the global well-posedness in L-2(T). The proof basically relies on the idea introduced in Takaoka-Tsutsumi's works [69,60], which weakens the non-trivial resonance in the cubic interactions (a kind of smoothing effect) for the local result, and the global well-posedness result immediately follows from L-2 conservation law. An immediate application of Takaoka-Tsutsumi's idea is available only in H-s (T ), s > 0, due to the lack of L-4-Strichartz estimate for arbitrary L-2 data, a slight modification, thus, is needed to attain the local well-posedness in L-2 (T). This is the first low regularity (global) well-posedness result for the periodic modified Kwahara equation, as far as we know. A direct interpolation argument ensures the unconditional uniqueness in H-s (T), s > 1/2, and as a byproduct, we show the weak ill-posedness below H1/2 (T), in the sense that the flow map fails to be uniformly continuous. (C) 2019 Elsevier Masson SAS. All rights reserved. | * |
dc.language | English | * |
dc.publisher | ELSEVIER | * |
dc.subject | Modified Kawahara equation | * |
dc.subject | Initial value problem | * |
dc.subject | Global well-posedness | * |
dc.subject | Unconditional uniqueness | * |
dc.subject | Weak ill-posedness | * |
dc.title | Well-posedness issues on the periodic modified Kawahara equation | * |
dc.type | Article | * |
dc.relation.issue | 2 | * |
dc.relation.volume | 37 | * |
dc.relation.index | SCIE | * |
dc.relation.index | SCOPUS | * |
dc.relation.startpage | 373 | * |
dc.relation.lastpage | 416 | * |
dc.relation.journaltitle | ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | * |
dc.identifier.doi | 10.1016/j.anihpc.2019.09.002 | * |
dc.identifier.wosid | WOS:000522121300005 | * |
dc.author.google | Kwak, Chulkwang | * |
dc.contributor.scopusid | 곽철광(55832871300) | * |
dc.date.modifydate | 20240311125607 | * |