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

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.
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Journal articles

Cited literature [26 references]

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 : Tuesday, June 19, 2018 - 3:50:01 PM
Long-term archiving on : Friday, August 22, 2014 - 11:36:09 AM

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• HAL Id : hal-00994815, version 1

### Citation

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⟩

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