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Local well-posedness and blow-up result for weakly dissipative Camassa-Holm equations. (English) Zbl 1326.35323

Summary: In this paper, we consider the Cauchy problem of the weakly dissipative Camassa-Holm equation. We prove the local well-posedness in the critical inhomogeneous Besov space \(B^{3/2}_{2,1}(\mathbb{R})\). This result depends on the apriori estimate of the nonlinear transport equation. Moreover, we show result for the finite time blowing up solution of the the weakly dissipative Camass-Holm equation which unifies previously known result. The proof relies on geometrical approach for the weakly dissipative Camass-Holm equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B44 Blow-up in context of PDEs
35B45 A priori estimates in context of PDEs
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Full Text: Euclid