Local well-posedness of the fifth-order KdV-type equations on the half-line

2018/08/16 by Márcio Cavalcante, Cavalcante, Márcio, Chulkwang Kwak +1
Mathematics · #35G31 #35Q53 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1808.06494

openalex publication_date 2018/08/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

This paper is a continuation of authors' previous work \citeCK2018-1. We extend the argument \citeCK2018-1 to fifth-order KdV-type equations with different nonlinearities, in specific, where the scaling argument does not hold. We establish the X^s,b nonlinear estimates for b < \frac12, which is almost optimal compared to the standard X^s,b nonlinear estimates for b > \frac12 \citeCGL2010, JH2009. As an immediate conclusion, we prove the local well-posedness of the initial-boundary value problem (IBVP) for fifth-order KdV-type equations on the right half-line and the left half-line.

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