# Randomization improved Strichartz estimates and global well-posedness for supercritical data

## TL;DR

This paper introduces a new randomization method for wave equation data that enhances Strichartz estimates in non-radial cases, enabling global well-posedness results for supercritical wave maps with small, randomized data.

## Contribution

The paper presents a novel data randomization technique that extends Strichartz estimates to non-radial data, leading to new global well-posedness results for supercritical wave equations.

## Key findings

- Enhanced Strichartz estimates for non-radial data
- Global well-posedness for supercritical wave maps with randomized data
- Applicable to small, supercritical initial data

## Abstract

We introduce a novel data randomisation for the free wave equation which leads to the same range of Strichartz estimates as for radial data, albeit in a non-radial context. We then use these estimates to establish global well-posedness for a wave maps type nonlinear wave equation for certain supercritical data, provided the data are suitably small and randomised.