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arXiv · 2011.01290

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

Nilay Duruk Mutlubas·Anna Geyer·Ronald Quirchmayr
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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 $H^s$ on the circle for $s>3/2$.

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Nilay Duruk Mutlubas, Anna Geyer, Ronald Quirchmayr. 2020-11-02. Well-posedness of a highly nonlinear shallow water equation on the circle. https://doi.org/10.1016/j.na.2020.111849

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