Archive for Rational Mechanics and Analysis

, Volume 212, Issue 1, pp 219–239 | Cite as

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

  • Eduard Feireisl
  • Antonín Novotný
  • Yongzhong Sun


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.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Eduard Feireisl
    • 1
  • Antonín Novotný
    • 2
  • Yongzhong Sun
    • 3
  1. 1.Faculty of Mathematics and Physics, Mathematical InstituteCharles University in PraguePrague 8Czech Republic
  2. 2.IMATH Université du Sud Toulon-VarLa GardeFrance
  3. 3.Department of MathematicsNanjing UniversityNanjingChina

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