Global Well-Posedness and Long-time Asymptotics for the Defocussing Davey-Stewartson II Equation in H^1,1(R²)

2011/10/25 by Perry, Peter A.
#35Q35 #37K15 #81U40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1110.5589

Abstract

We show that the inverse scattering map for the linear system associated with the defocussing Davey-Stewartson II equation is locally Lipschitz continuous with locally Lipschitz continuous inverse on H^1,1(R²). From the inverse scattering method we then obtain global well-posedness for the defocussing Davey-Stewartson II equation. We show that these global solutions are dispersive by computing their leading asymptotic behavior as t → ∞ in terms of an associated linear problem.

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