Sharp blow-up criteria for the Davey-Stewartson system in ℝ3

Abstract

In this paper, we study the blow-up solutions for the Davey- Stewartson system iut + Δu + |u|p-1u + E(|u|2)u = 0, t ≥ 0, x ∈ ℝ3. (DS) Using the profile decomposition of the bounded sequences in H1(ℝ3), we give some new variational characteristics for the ground states and generalized Gagliardo-Nirenberg inequalities. Then, we obtain the precise expressions on the sharp blow-up criteria to (DS) for 1 + 4/3 ≤ p < 5. © 2011 International Press.