Blow-up phemomenon for the 3-component Degasperis-Procesi equation
Song Liu, Zhaoyang Yin
TL;DR
This paper investigates the blow-up phenomena of the 3-component Degasperis-Procesi equation, establishing conditions for blow-up, local well-posedness, and persistence properties without relying on conservation laws.
Contribution
It provides new insights into blow-up behavior and persistence properties of solutions to the 3-component Degasperis-Procesi equation without conservation law assumptions.
Findings
Blow-up criteria established in low Besov spaces
Method developed that does not depend on conservation laws
Persistence properties of solutions analyzed
Abstract
In this paper, we consider the Cauchy problem of the 3-component Degasperis-Procesi equation. Firstly, we discuss a local well-posedness result and a blow-up criterion in the low besov space. Secondly, we study the blow-up phenomenon by using the method which does not require any conservation law. Finally, we investigate some persistence properties.
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Taxonomy
TopicsNavier-Stokes equation solutions · Nonlinear Waves and Solitons · Nonlinear Partial Differential Equations