Blow-up in several points for the Davey–Stewartson system in R2

Abstract In this paper, we study the blow-up solutions for the Davey–Stewartson system in R 2 , which appears in the description of the evolution of surface water waves. For any given points x 1 , … , x p in R 2 , 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 { x 1 , … , x p } and in R 2 ∖ { x 1 , … , x p } . Our result gives a rigorous analysis for the numerical result of Besse et al. in [2] .