Abstract : 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.
https://hal-univ-tln.archives-ouvertes.fr/hal-00994815
Contributor : Antonin Novotny <>
Submitted on : Thursday, May 22, 2014 - 11:03:03 AM Last modification on : Wednesday, November 18, 2020 - 7:20:08 PM Long-term archiving on: : Friday, August 22, 2014 - 11:36:09 AM
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, Springer Verlag, 2014, 212 (1), pp.219-239. ⟨hal-00994815⟩