Weak-strong uniqueness property for the full Navier-Stokes-Fourier system

TL;DR

This paper proves that weak solutions to the full Navier-Stokes-Fourier system are unique when a strong solution exists, establishing a weak-strong uniqueness property for compressible, heat-conducting fluids.

Contribution

It demonstrates the weak-strong uniqueness principle for the full Navier-Stokes-Fourier system, ensuring weak solutions coincide with strong solutions when both exist from the same initial data.

Findings

Weak solutions coincide with strong solutions when the latter exists.

Strong solutions are unique within the class of weak solutions.

The result applies to the full Navier-Stokes-Fourier system for compressible fluids.

Abstract

The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within the class of weak solutions.