Blow-up phenomena and the local well-posedness of a Two-Component b-Family Equations in Besov spaces

TL;DR

This paper investigates the local well-posedness and blow-up phenomena of a Two-Component b-Family equation within Besov spaces, providing new insights into the equation's behavior and solution stability.

Contribution

The paper establishes local well-posedness in Besov spaces and introduces a novel blow-up result for the Two-Component b-Family equations.

Findings

Proved local well-posedness in $B^{1+rac 1 p}_{p,1}$ spaces.

Derived a new blow-up criterion for solutions.

Enhanced understanding of solution behavior in Besov spaces.

Abstract

In this paper, we first establish the local well-posednesss of a Two-Component b-Family equations in nonhomogeneous Besov spaces $B^{1+\frac 1 p}_{p,1}$ with $1\leq p<+\infty.$ Then we present a new blow-up result for the Two-Component b-Family equations.