Wave breaking phenomena and global existence for the weakly dissipative generalized Camassa-Holm equation
Keyword(s):
Blow Up
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<p style='text-indent:20px;'>In this paper, we mainly study several problems on the weakly dissipative generalized Camassa-Holm equation. We first establish the local well-posedness of solutions by Kato's semigroup theory. We then derive the necessary and sufficient condition of the blow-up of solutions and a criteria to guarantee occurrence of wave breaking. Moreover, when the solution blows up, we obtain the precise blow-up rate. We finally show that the equation has a unique global solution provided the moment density associated with their initial datum satisfies appropriate sign conditions.</p>