Well-posedness of a kind of the free surface equation of shallow water waves

Zhouyu Li; MiaoMiao Dang

doi:10.1216/rmj.2020.50.1409

Abstract

For the Cauchy problem of the one-dimensional free surface equation of shallow water waves, we obtain local well-posedness of the free surface equation of shallow water waves in Sobolev spaces. We also derive a wave-breaking mechanism for strong solutions.

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Zhouyu Li. MiaoMiao Dang. "Well-posedness of a kind of the free surface equation of shallow water waves." Rocky Mountain J. Math. 50 (4) 1409 - 1423, August 2020. https://doi.org/10.1216/rmj.2020.50.1409

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Received: 31 October 2019; Accepted: 9 January 2020; Published: August 2020

First available in Project Euclid: 29 September 2020

zbMATH: 07261871

MathSciNet: MR4154814

Digital Object Identifier: 10.1216/rmj.2020.50.1409

Subjects:

Primary: 35G25 , 35Q58

Keywords: local well-posedness , shallow water , wave-breaking

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