Energy scattering of a modified Davey–Stewartson system in three dimensions. Issue 5 (24th March 2023)

• Record Type: Journal Article
• Authors: Lu, Jing; Tang, Xingdong
• Is Part Of: Applicable analysis. Volume 102:Issue 5(2023)
• Page Start: 1490
• Page End: 1510
• Publication Date: 2023-03-24
• Subjects: Davey–Stewartson system -- scatter -- global well-posedness -- profile decomposition; Primary: 35Q55 -- Secondary: 47J35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1989417
• Languages: English
• ISSNs: 0003-6811

Abstract

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.