Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

Abstract

This paper is concerned with the Cauchy problem of $2$D Klein-Gordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get the local in time well-posedness. The estimates are established by the Fourier restriction norm method. We utilize the bilinear Strichartz estimates and the nonlinear version of the classical Loomis-Whitney inequality which was applied to Zakharov system.

References in corpus (3)

• Convolutions of singular measures and applications to the Zakharov system
• A convolution estimate for two-dimensional hypersurfaces
• Local ill-posedness of the 1D Zakharov system