Blow-up phemomenon for the Geng-Xue system and related models

TL;DR

This paper investigates the blow-up phenomena in the Geng-Xue system with cubic nonlinearity, establishing criteria for blow-up and extending results to related two-component systems without relying on conservation laws.

Contribution

It provides new blow-up criteria in low Besov spaces and demonstrates blow-up phenomena without conservation laws, extending to related models.

Findings

Blow-up criteria established in low Besov spaces

Blow-up phenomena proved without conservation laws

Results extended to related two-component systems

Abstract

In this paper, we consider the Cauchy problem of the Geng-Xue system with cubic nonlinearity. Firstly, we prove a blow-up criteria in the low besov space. Secondly, we prove the blow-up phenomenon by using the method which does not require any conservation law. Finally, we extend our results to the b-family of two-component system with cubic nonlinearity.