# Local well-posedness of the vacuum free boundary of 3-D compressible Navier-Stokes equations

## TL;DR

This paper proves local well-posedness for the 3-D viscous gas equations with vacuum free boundary, using conormal derivatives and avoiding strong initial data compatibility conditions.

## Contribution

It introduces a novel approach to establish well-posedness without requiring strong compatibility conditions on initial data.

## Key findings

- Established local well-posedness of the 3-D viscous gas with vacuum boundary
- Used conormal derivatives to handle boundary regularity
- Removed the need for strong initial data compatibility conditions

## Abstract

In this paper, we consider the 3-D motion of viscous gas with the vacuum free boundary. We use the conormal derivative to establish local well-posedness of this system. One of important advantages in the paper is that we do not need any strong compatibility conditions on the initial data in terms of the acceleration.