# Weighted gevrey class regularity of euler equation in the whole space

## TL;DR

This paper investigates the weighted Gevrey class regularity of the Euler equations in three-dimensional space, establishing local existence and regularity results using weighted Sobolev-Gevrey spaces and novel estimates for pressure terms.

## Contribution

It introduces a new approach combining weighted Sobolev-Gevrey spaces and singular operator properties to improve regularity analysis of Euler equations.

## Key findings

- Proved local existence of solutions in weighted Sobolev spaces.
- Established weighted Gevrey regularity for Euler equations.
- Enhanced pressure term estimates using singular operator properties.

## Abstract

In this paper we study the weighted Gevrey class regularity of Euler equation in the whole space R 3. We first establish the local existence of Euler equation in weighted Sobolev space, then obtain the weighted Gevrey regularity of Euler equation. We will use the weighted Sobolev-Gevrey space method to obtain the results of Gevrey regularity of Euler equation, and the use of the property of singular operator in the estimate of the pressure term is the improvement of our work.