A Regularity Criterion for the Weak Solutions to the Navier-Stokes-Fourier System

Eduard Feireisl (1) , Antonin Novotny (2) , Yongzhong Sun (3)

1 Mathematical Institute [Praha] - Academy of Sciences
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 Department of Mathematics

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

Domaines: Equations aux dérivées partielles [math.AP]

Eduard Feireisl, Antonin Novotny, Yongzhong Sun. A Regularity Criterion for the Weak Solutions to the Navier-Stokes-Fourier System. Archive for Rational Mechanics and Analysis, 2014, 212 (1), pp.219-239. ⟨hal-00994815⟩