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A Regularity Criterion for the Weak Solutions to the Navier–Stokes–Fourier System |
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| Authors: | Eduard Feireisl Antonín Novotný Yongzhong Sun |
| Institution: | 1. Faculty of Mathematics and Physics, Mathematical Institute, Charles University in Prague, Sokolovská 83, 186 75, Prague 8, Czech Republic 2. IMATH Université du Sud Toulon-Var, BP 132, 83957, La Garde, France 3. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu, China |
| Abstract: | 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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