Blow-up phenomena for the rotation-two-component Camassa–Holm system

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...

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

Blow-Up Phenomena and Decay for the Periodic Degasperis-Procesi Equation with Weak Dissipation

In the paper, several problems on the periodic Degasperis-Procesi equation with weak dissipation are investigated. At first, the local well-posedness of the equation is established by Kato’s theorem and a precise blow-up scenario of the solutions is given. Then, several criteria guaranteeing the blow-up of the solutions are presented. Moreover, the blow-up rate and blow-up set of the blowing-up...

Blow-up Conditions for Two Dimensional Modified Euler-poisson Equations

The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow-up for some initial configurations. This article strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional modified EulerPoisson system with a modified Riesz transform where the singular...

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.