Well-posedness of a highly nonlinear shallow water equation on the circle

Journal article (2020)

Authors

Nilay Duruk Mutlubas Sabanci University

A. Geyer Mathematical Physics -

Ronald Quirchmayr KTH Royal Institute of Technology

Research Group

Mathematical Physics () (TU Delft)

Shallow water equation Cubic nonlinearity Large amplitude waves Well-posedness

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Published Date

01-08-2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space Hs on the circle for s>3∕2.

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