Local well-posedness of the Cauchy problem for the degenerate Zakharov system

TL;DR

This paper establishes local well-posedness for the degenerate Zakharov system's Cauchy problem using anisotropic Sobolev spaces and advanced function space techniques, expanding understanding of its mathematical properties.

Contribution

It proves local well-posedness for the degenerate Zakharov system with specific anisotropic Sobolev initial data using $U^2, V^2$ spaces, a novel approach for this system.

Findings

Local well-posedness established for anisotropic Sobolev data.

Application of $U^2, V^2$ spaces to the degenerate Zakharov system.

Conditions on initial data regularity for well-posedness.

Abstract

The aim of this paper is to investigate well-posedness of the Cauchy problem for the degenerate Zakharov system. Local well-posedness holds for anisotropic Sobolev data by applying $U^2, V^2$ type spaces. We give the Schr\"odinger initial data $H^{s_k, s'}$ and the wave data $H^{s_l, s'}$ where $s_k > (d-1)/2, s_l > (d-2)/2, s_k - s_l = 1/2$ and $s' > 1/2$.