The Cauchy problem and wave-breaking phenomenon for a generalized sine-type FORQ/mCH equation
arXiv:2112.10772 · doi:10.1007/s00605-021-01633-6
Abstract
In this paper, we are concerned with the Cauchy problem and wave-breaking phenomenon for a sine-type modified Camassa-Holm (alias sine-FORQ/mCH) equation. Employing the transport equations theory and the Littlewood-Paley theory, we first establish the local well-posedness for the strong solutions of the sine-FORQ/mCH equation in Besov spaces. In light of the Moser-type estimates, we are able to derive the blow-up criterion and the precise blow-up quantity of this equation in Sobolev spaces. We then give a sufficient condition with respect to the initial data to ensure the occurance of the wave-breaking phenomenon by trace the precise blow-up quantity along the characteristics associated with this equation.
17 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2112.10361