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

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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

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10.1016/j.physd.2019.132208

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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).

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KW - Restricted norm method

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

Abstract

Keywords

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