On the Cauchy problem of a two-component b-family equation

Abstract

In this paper, we study the Cauchy problem of a two-component b-family equation. We first establish the local well-posedness for a two-component b-family equation by Kato's semigroup theory. Then, we derive precise blow-up scenarios for strong solutions to the equation. Moreover, we present several blow-up results for strong solutions to the equation.