Eduard Feireisl, Antonin Novotny, Yongzhong Sun
Published 2012-09-15Version 1
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.
Uniqueness criterion of weak solutions for the 3D Navier-Stokes equations
New regularity criteria for NSE and SQG in critical spaces
Regularity of a Weak Solution to the Navier-Stokes Equations via One Component of a Spectral Projection of Vorticity
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