No pure capillary solitary waves exist in 2D finite depth

2021/04/16 by Mihaela Ifrim, Ben Pineau, Ifrim, Mihaela +5
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2104.07845

openalex publication_date 2021/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the 2D finite depth capillary water wave equations admit no solitary wave solutions. This closes the existence/non-existence problem for solitary water waves in 2D, under the classical assumptions of incompressibility and irrotationality, and with the physical parameters being gravity, surface tension and the fluid depth.

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