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arXiv · 2511.06007

The Kawahara equation on star graphs

Márcio Cavalcante·Chulkwang Kwak·José Marques
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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.

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Márcio Cavalcante, Chulkwang Kwak, José Marques. 2025-11-08. The Kawahara equation on star graphs. https://arxiv.org/abs/2511.06007

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