Attractors for the viscous Camassa-Holm equation

2006/12/12 by Milena Stanislavova, Stanislavova, Milena, Atanas Stefanov +1
Mathematics · Physics and Astronomy · #35B41 #35B65 #35Q35 #35Q58 #37K40 #76B15 #Advanced Mathematical Physics Problems #Applied mathematics #Attractor #Camassa–Holm equation #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical analysis #Mathematical economics #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.DS #msc:35B41 #msc:35B65 #msc:35Q35 #msc:35Q58 #msc:37K40 #msc:76B15

paper · pdf · doi:10.48550/arxiv.math/0612321

published in arXiv (Cornell University) (Cornell University) · To appear in DCDS- A

arxiv created 2006/12/12 · openalex publication_date 2006/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that the viscous Camassa-Holm equation subject to an external force, and where the viscosity term is given by second order differential operator in divergence form has a global attractors in the energy space H¹. Moreover, we establish an asymptotic smoothing effect.

Citations

• Wave breaking for nonlinear nonlocal shallow water equations

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