Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons

Abstract

Considered herein is a modified two-component periodic Camassa-Holm system with peakons. The local well-posedness and low regularity result of solutions are established. The precise blow-up scenarios of strong solutions and several results of blow-up solutions with certain initial profiles are described in detail and the exact blow-up rate is also obtained.

Wave-Breaking and Peakons for a Modified Camassa–Holm Equation

“…Using the first Moser-type estimate in (4.1) and the Sobolev embedding inequality, we have 21) where the genius constant ε 0 ∈ (0, …”

“…An alternative modified CH equation was introduced in [26]. Multi-component versions of the CH equation have been introduced and studied in [15,21,27,31,32,33,48].…”

Wave Breaking and Measure of Momentum Support for an Integrable Camassa‐Holm System with Two Components

“…For convenience, we call the CH2 equation. It appears initially in , and its mathematical properties have been studied further in many works . Recently, Constantin and Ivanov in gave a demonstration about its derivation in view of shallow water theory from the hydrodynamic point of view.…”

“…For convenience, we call (1) the CH2 equation. It appears initially in [1], and its mathematical properties have been studied further in many works [2][3][4][5][6].…”

Well-Posedness and Analyticity for an Integrable Two-Component System With Cubic Nonlinearity

“…An alternative modified Camassa-Holm equation was introduced in [22,35]. Multicomponent versions of the Camassa-Holm equation have been introduced and studied in [19,23,24,[28][29][30]13]. Motivated by the references cited above, the goal of the present paper is to establish the local well-posedness for the strong solutions to the Cauchy problem (1.1).…”