Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations

2009/11/17 by Hailiang Liu, Zhaoyang Yin, Liu, Hailiang +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0911.3404

openalex publication_date 2009/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with a class of nonlocal dispersive models -- the θ-equation proposed by H. Liu [ On discreteness of the Hopf equation, \it Acta Math. Appl. Sin. Engl. Ser. \bf 24(3)(2008)423--440]: (1-∂_x²)u_t+(1-θ∂_x²)((u²)/(2))_x =(1-4θ)((u_x²)/(2))_x, including integrable equations such as the Camassa-Holm equation, θ=1/3, and the Degasperis-Procesi equation, θ=1/4, as special models. We investigate both global regularity of solutions and wave breaking phenomena for θ∈ ℝ. It is shown that as θ increases regularity of solutions improves: (i) 0

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