Well-posedness and scattering for the Zakharov system in four dimensions

Abstract

The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are proved, including the case of initial data in the energy space. None of these results is restricted to radially symmetric data.

25 pages, 2 figures

References in corpus (6)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Convolutions of singular measures and applications to the Zakharov system
• On the 2d Zakharov system with L^2 Schrödinger data
• Small energy scattering for the Zakharov system with radial symmetry
• Scattering for the Zakharov system in 3 dimensions
• Generalized Strichartz estimates and scattering for 3D Zakharov system

Cited by in corpus (3)

• Global wellposedness for the energy-critical Zakharov system below the ground state
• Local Well-Posedness for the Zakharov System in Dimension $d⩽3$
• The three dimensional stochastic Zakharov system