Regularity criterion via two components of velocity on weak solutions to the shear thinning fluids in R3

We consider the regularity of weak solutions to the shear thinning fluids in R3. Let u be a weak solution in R3× (0 , T) and u~ = (u1, u2, 0). It is proved that u becomes a strong solution if u~∈L5p-65p-8(0,T;BMO(R3)) , for 85<p≤2. This is an improvement of the result given by Yang (Comput Math Appl 77:2854–2858). © 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.