The Kawahara equation on star graphs

2025/11/08 by Márcio Cavalcante, Cavalcante, Márcio, Chulkwang Kwak +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2511.06007

Abstract

In this paper, we establish local well-posedness for the Cauchy problem associated with the Kawahara equation on a general metric star graph. Initially, we identify suitable boundary conditions that produce a well-behaved dynamics for the linear equation. Subsequently, we derive the integral formula using the forcing operator method, previously applied to the Kawahara equation on the half-line by Cavalcante and Kwak (NoDEA 2020), and the Fourier restriction method of Bourgain (GAFA 1993). This work has the potential to be extended to other fifth-order nonlinear dispersive equations on star graphs.

Citations

• The linearized Korteweg-de Vries equation on the line with metric graph defects
• The initial-boundary value problem for the Kawahara equation on the half-line
• Global well-posedness and I-method for the fifth-order Korteweg-de Vries equation
• The initial-boundary value problem for the Korteweg-de Vries equation
• The generalized Korteweg-de Vries equation on the half line

Cited by

• A Nonhomogeneous Boundary-Value Problem For The Nonlinear KdV Equation on Star Graphs

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• The initial-boundary value problem for the Kawahara equation on the half-line