A Regularity Criterion for the Weak Solutions to the Navier-Stokes-Fourier System - Archive ouverte HAL Access content directly
Journal Articles Archive for Rational Mechanics and Analysis Year : 2014

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

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Eduard Feireisl
• Function : Author
Antonin Novotny
Yongzhong Sun
• Function : Author

#### 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.

#### Domains

Mathematics [math] Analysis of PDEs [math.AP]

### Dates and versions

hal-00994815 , version 1 (22-05-2014)

### Identifiers

• HAL Id : hal-00994815 , version 1

### Cite

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⟩

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