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

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...

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Bibliographic Details
Published in:Physica. D 2020-01, Vol.402, p.132208, Article 132208
Main Authors: Compaan, E., Tzirakis, N.
Format: Article
Language:English
Subjects:
gKdV system initial–boundary value problems
KdV system
Restricted norm method
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Summary: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). •Functional analytic methods concerning the well-posedness theory of initial and boundary value problems .•Existence and uniqueness properties for a Korteweg–de Vries type equation on a semi-infinite interval.•Fourier and Laplace transform methods.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2019.132208