Local Well-Posedness for the Zakharov System in Dimension $d⩽3$

Abstract

The Zakharov system in dimension $d⩽3$ is shown to be locally well-posed in Sobolev spaces $H^s\times H^l$, extending the previously known result. We construct new solution spaces by modifying the $X^{s,b}$ spaces, specifically by introducing temporal weights. We use contraction mapping principle to prove local well-posedness in the same. The result obtained is sharp up to endpoints.

26 pages, 2 figures

References in corpus (4)

• Convolutions of singular measures and applications to the Zakharov system
• On the 2d Zakharov system with L^2 Schrödinger data
• Local ill-posedness of the 1D Zakharov system
• Small energy scattering for the Zakharov system with radial symmetry

Cited by in corpus (2)

• The three dimensional stochastic Zakharov system
• Local well-posedness of a system describing laser-plasma interactions