Well-posedness of a highly nonlinear shallow water equation on the circle
Duruk Mutlubaş, Nilay and Geyer, Anna and Quirchmayr, Ronald (2020) Well-posedness of a highly nonlinear shallow water equation on the circle. Nonlinear Analysis: Theory, Methods & Applications, 197 . ISSN 0362-546X (Print) 1873-5215 (Online)
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Official URL: http://dx.doi.org/10.1016/j.na.2020.111849
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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