Scattering for the Zakharov system in 3 dimensions

Abstract

We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t^{-1}, whereas the Schrödinger component decays almost at a rate of t^{-7/6}.

Minor changes and referee's comments included

References in corpus (2)

• Convolutions of singular measures and applications to the Zakharov system
• On the 2d Zakharov system with L^2 Schrödinger data

Cited by in corpus (8)

• The Euler--Maxwell system for electrons: global solutions in $2D$
• Modified scattering for the Boson Star Equation
• Generalized Strichartz estimates and scattering for 3D Zakharov system
• The fourth order nonlinear Schrodinger limit for quantum Zakharov system
• Well-posedness and scattering for the Zakharov system in four dimensions
• On the Global Stability of a Beta-Plane Equation
• The three dimensional stochastic Zakharov system
• Long time decay and asymptotics for the complex mKdV equation