Advances in Differential Equations

Local well-posedness and blow-up result for weakly dissipative Camassa-Holm equations

Sungyong Park

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Abstract

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.

Article information

Source
Adv. Differential Equations Volume 20, Number 9/10 (2015), 983-1008.

Dates
First available in Project Euclid: 23 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1435064519

Mathematical Reviews number (MathSciNet)
MR3360397

Zentralblatt MATH identifier
1326.35323

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Citation

Park, Sungyong. Local well-posedness and blow-up result for weakly dissipative Camassa-Holm equations. Adv. Differential Equations 20 (2015), no. 9/10, 983--1008. https://projecteuclid.org/euclid.ade/1435064519.


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