Sharp well-posedness for the generalized KdV of order three on the half line

E. Compaan; N. Tzirakis

doi:10.1016/j.physd.2019.132208

Sharp well-posedness for the generalized KdV of order three on the half line

E. Compaan
, N. Tzirakis

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we study the generalized Korteweg–de Vries (KdV) equation with the nonlinear term of order three: (u³⁺¹)_x. We prove sharp local well-posedness for the initial and boundary value problem posed on the right half line. We thus close the gap in the well-posedness theory of the generalized KdV which remained open after the seminal work of Colliander and Kenig in Colliander and Kenig (2002).

Original language	English (US)
Article number	132208
Journal	Physica D: Nonlinear Phenomena
Volume	402
DOIs	https://doi.org/10.1016/j.physd.2019.132208
State	Published - Jan 15 2020

Keywords

KdV system
Restricted norm method
gKdV system initial–boundary value problems

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Online availability

10.1016/j.physd.2019.132208

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title = "Sharp well-posedness for the generalized KdV of order three on the half line",

abstract = "In this paper we study the generalized Korteweg–de Vries (KdV) equation with the nonlinear term of order three: (u3+1)x. We prove sharp local well-posedness for the initial and boundary value problem posed on the right half line. We thus close the gap in the well-posedness theory of the generalized KdV which remained open after the seminal work of Colliander and Kenig in Colliander and Kenig (2002).",

keywords = "KdV system, Restricted norm method, gKdV system initial–boundary value problems",

author = "E. Compaan and N. Tzirakis",

note = "We thank Prof. Bingyu Zhang for useful discussions regarding this problem. The first author was supported by NSF MSPRF, United States of America \#1704865 . The second author{\textquoteright}s work was supported by a grant from the Simons Foundation ( \#355523 Nikolaos Tzirakis) and the Illinois Research Board, United States of America RB18051 . We thank Prof. Bingyu Zhang for useful discussions regarding this problem. The first author was supported by NSF MSPRF, United States of America\#1704865. The second author's work was supported by a grant from the Simons Foundation (\#355523 Nikolaos Tzirakis) and the Illinois Research Board, United States of AmericaRB18051.",

year = "2020",

month = jan,

day = "15",

doi = "10.1016/j.physd.2019.132208",

language = "English (US)",

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journal = "Physica D: Nonlinear Phenomena",

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T1 - Sharp well-posedness for the generalized KdV of order three on the half line

AU - Compaan, E.

AU - Tzirakis, N.

N1 - We thank Prof. Bingyu Zhang for useful discussions regarding this problem. The first author was supported by NSF MSPRF, United States of America #1704865 . The second author’s work was supported by a grant from the Simons Foundation ( #355523 Nikolaos Tzirakis) and the Illinois Research Board, United States of America RB18051 . We thank Prof. Bingyu Zhang for useful discussions regarding this problem. The first author was supported by NSF MSPRF, United States of America#1704865. The second author's work was supported by a grant from the Simons Foundation (#355523 Nikolaos Tzirakis) and the Illinois Research Board, United States of AmericaRB18051.

PY - 2020/1/15

Y1 - 2020/1/15

N2 - In this paper we study the generalized Korteweg–de Vries (KdV) equation with the nonlinear term of order three: (u3+1)x. We prove sharp local well-posedness for the initial and boundary value problem posed on the right half line. We thus close the gap in the well-posedness theory of the generalized KdV which remained open after the seminal work of Colliander and Kenig in Colliander and Kenig (2002).

AB - In this paper we study the generalized Korteweg–de Vries (KdV) equation with the nonlinear term of order three: (u3+1)x. We prove sharp local well-posedness for the initial and boundary value problem posed on the right half line. We thus close the gap in the well-posedness theory of the generalized KdV which remained open after the seminal work of Colliander and Kenig in Colliander and Kenig (2002).

KW - KdV system

KW - Restricted norm method

KW - gKdV system initial–boundary value problems

UR - https://www.scopus.com/pages/publications/85073530227

UR - https://www.scopus.com/pages/publications/85073530227#tab=citedBy

U2 - 10.1016/j.physd.2019.132208

DO - 10.1016/j.physd.2019.132208

M3 - Article

AN - SCOPUS:85073530227

SN - 0167-2789

VL - 402

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

M1 - 132208

ER -

Sharp well-posedness for the generalized KdV of order three on the half line

Abstract

Keywords

ASJC Scopus subject areas

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