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Well-posedness, blowup, and global existence for an integrable shallow water equation
We establish the local well-posedness for a
recently derived model that combines the linear dispersion of
Korteweg-de Veris equation with the nonlinear/nonlocal dispersion
of the Camassa-Holm equation, and we prove that the equation has
solutions that exist for indefinite times as well as solutions
that blow up in finite time. We also derive an explosion criterion
for the equation, and we give a sharp estimate of the existence
time for solutions with smooth initial data.