We show some regularity criteria for Navier-Stokes equations, the harmonic heat flow, two liquid crystals models, and a model for magneto-elastic materials. The method of proof depends on a systematic use of interpolation inequalities in Besov spaces and is independent on logarithmic inequalities.
Jishan Fan. Tohru Ozawa. "Regularity criteria for Navier-Stokes and related system." Differential Integral Equations 30 (1/2) 101 - 114, January/February 2017. https://doi.org/10.57262/die/1484881221