Low regularity global well-posedness for the two-dimensional Zakharov system

TL;DR

This paper proves the global well-posedness of the 2D Zakharov system for low-regularity initial data with small L^2 norm, using a refined I-method and establishing polynomial growth bounds.

Contribution

It introduces a refined I-method approach to establish global solutions for the 2D Zakharov system with minimal regularity assumptions.

Findings

Global solutions exist for small L^2 initial data

Polynomial growth bounds are established for solutions

Unique solutions are guaranteed without finite energy constraints

Abstract

The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L^2 - norm of the Schr\"odinger part is small enough. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffilani, Takaoka and Tao. A polynomial growth bound for the solution is also given.