Absence of anomalous dissipation for weak solutions of the Maxwell--Stefan system

TL;DR

This paper proves that weak solutions to the Maxwell-Stefan system inherently satisfy an entropy equality, confirming the absence of anomalous energy dissipation in such solutions.

Contribution

It provides a concise, self-contained proof that weak solutions to the Maxwell-Stefan system do not exhibit anomalous dissipation, reinforcing the system's physical consistency.

Findings

Weak solutions satisfy an entropy equality

No anomalous dissipation occurs in the system

Proof is concise and self-contained

Abstract

In this paper we give a short and self-contained proof of the fact that weak solutions to the Maxwell-Stefan system automatically satisfy an entropy equality, establishing the absence of anomalous dissipation.