On the Cauchy problem of a weakly dissipative μHS equation

2011/08/23 by Jingjing Liu, Zhaoyang Yin, Liu, Jingjing +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.1108.4550

openalex publication_date 2011/08/23 · arxiv created 2011/09/13 · arxiv updated 2011/09/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Cauchy problem of a weakly dissipative μHS equation. We first establish the local well-posedness for the weakly dissipative μHS equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.

Citations

• Global Conservative Solutions of the Camassa–Holm Equation
• Global existence and blow-up phenomena for the weakly dissipative Camassa–Holm equation
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations
• Wave breaking for nonlinear nonlocal shallow water equations
• On the Blow-Up of Solutions of a Periodic Shallow Water Equation

Related

• Global weak solutions to a weakly dissipative μHS equation
• New results on the global solvability and blow-up for a class of weakly dissipative Camassa-Holm equations
• On the Cauchy problem for a weakly dissipative Camassa-Holm equation in critical Besov spaces
• On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation
• On uniqueness of dissipative solutions of the Camassa-Holm equation