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Well-posedness of a highly nonlinear shallow water equation on the circle. (English) Zbl 1434.35090

Summary: 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 \(s > 3 / 2\).

MSC:

35Q35 PDEs in connection with fluid mechanics
35L30 Initial value problems for higher-order hyperbolic equations
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