A regularity criterion for the weak solutions to the Navier-Stokes-Fourier system

Abstrakt

We show that any weak solution to the full Navier-Stokes-Fourier system emanating from the data belonging to the Sobolev space $W^{3,2}$ remains regular as long as the velocity gradient is bounded. The proof is based on the weak-strong uniqueness property and parabolic a priori estimates for the local strong solutions.

Klíčová slova

• regularity criterion
• weak solutions
• Navier-Stokes-Fourier system