Energy scattering of a modified Davey–Stewartson system in three dimensions. Issue 5 (24th March 2023) - Lu, Jing; Tang, Xingdong
Abstract : We obtain the global well-posedness and the scattering theory of the solution for the modified Davey–Stewartson system 1 i ∂ t u + Δ u = | u | 4 u + u v x 1, ( t, x ) ∈ R × R 3, − Δ v = ( | u | 2 ) x 1 in the energy space H 1 ( R 3 ) in this paper. Since the interaction Morawetz estimate fails and the nonlinearity is non-local, we employ the concentration-compactness argument introduced by Kenig and Merle (Invent Math. 2006;166:645–675) to establish the scattering result.,