Abstract
We derive a quasilinear shallow water equation directly from the governing equations for gravity water waves within a certain regime for large-amplitude waves which has not been studied so far. Furthermore, we demonstrate local well-posedness of the corresponding Cauchy problem and finally discuss some aspects of the blowup behavior of solutions.
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Quirchmayr, R. A new highly nonlinear shallow water wave equation. J. Evol. Equ. 16, 539–567 (2016). https://doi.org/10.1007/s00028-015-0312-4
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DOI: https://doi.org/10.1007/s00028-015-0312-4