# Uniqueness of Solutions to a Gas-Disk Interaction System

## TL;DR

This paper provides the first rigorous proof of the uniqueness of solutions to a gas-disk interaction system with diffusive boundary conditions, applicable even far from equilibrium states.

## Contribution

It establishes the uniqueness of solutions under minimal regularity assumptions, addressing an open problem in the mathematical analysis of gas-disk systems.

## Key findings

- Proves uniqueness of solutions with locally Lipschitz regularity.
- Applicable to solutions far from equilibrium.
- Addresses an open problem in the field.

## Abstract

In this paper we give an elementary proof of uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. Existence of near-equilibrium solutions for this type of systems with various boundary conditions has been extensively studied in [1-8, 10]. However, the uniqueness has been an open problem, even for solutions near equilibrium. Our work gives the first rigorous proof of the uniqueness among solutions that are only required to be locally Lipschitz; in particular, it holds for solutions far from equilibrium states.