Blow-up in several points for the Davey–Stewartson system in [formula omitted

Abstract

In this paper, we study the blow-up solutions for the Davey–Stewartson system in R2, which appears in the description of the evolution of surface water waves. For any given points x1,…,xp in R2, we construct a solution u(t) which blows up in finite time T exactly in these points. In addition, we investigate the precise behavior of the solution u(t) as t→T both at the blow-up points {x1,…,xp} and in R2∖{x1,…,xp}. Our result gives a rigorous analysis for the numerical result of Besse et al. in [2].