Blow-up analysis for a periodic two-component μ-Hunter–Saxton system

On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

Global weak solutions for a periodic two-component μ-Hunter-Saxton system

This paper is concerned with global existence of weak solutions for a periodic twocomponent μ-Hunter-Saxton system. We first derive global existence for strong solutions to the system with smooth approximate initial data. Then, we show that the limit of approximate solutions is a global weak solution of the two-component μ-Hunter-Saxton system. 2000 Mathematics Subject Classification: 35G25, 35L05

Local Well-posedness and Blow-up Phenomenon for a Modified Two-component Camassa-Holm System in Besov Spaces

ρt + (uρ)x = 0, t > 0, x ∈ R, (1.1b) m(0, x) = m0(x), x ∈ R, (1.1c) ρ(0, x) = ρ0(x), x ∈ R, (1.1d) where (u0, ρ0) is given modified profile,m = u−uxx and ρ = (1−∂ x)(ρ−ρ0) ,g is a positive constant. For convenience, we let g = 1 in this paper. The modified two-component Camassa-Holm equation is written in terms of velocityu and locally averaged density ρ . With m = u− uxx ,ρ = γ − γxx and γ = ρ...

Periodic Conservative Solutions for the Two-component Camassa–holm System

We construct a global continuous semigroup of weak periodic conservative solutions to the two-component Camassa–Holm system, ut − utxx + κux + 3uux − 2uxuxx − uuxxx + ηρρx = 0 and ρt + (uρ)x = 0, for initial data (u, ρ)|t=0 in H1 per ×Lper. It is necessary to augment the system with an associated energy to identify the conservative solution. We study the stability of these periodic solutions by...

A Blow-up Result for a Viscoelastic System in R

In this paper we consider a coupled system of nonlinear viscoelastic equations. Under suitable conditions on the initial data and the relaxation functions, we prove a finite-time blow-up result.