Local well-posedness and global existence for the Popowicz system

2022/02/23 by Wei Tan, Zhaoyang Yin, Tan, Wei +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2202.11362

openalex publication_date 2022/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Popowicz system, as the interacting system of Camassa-Holm and Degasperis-Procesi equations, has attracted some attention in recent years. In this paper, we first study the local well-posedness for the cauchy problem of Popowicz system in nonhomogeneous Besov spaces B^s_p,r× B^s_p,r with s> max\2, (1)/(p)+(3)/(2)\ or (s=2, 2≤ p ≤ ∞, 1≤ r≤ 2). Moreover, a new blow-up criterion and global existence with different initial values are obtained.

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