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 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

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

openalex publication_date 2006/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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