Local Regularity Criteria for the 3D Co-rotational Beris-Edwards System in Lorentz Spaces

In this paper, we present some new regularity criteria for suitable weak solutions to the 3D co-rotational Beris-Edwards system. First, we prove that suitable weak solutions are regular if the scaled Lp;q-norm of the velocity field or gradient of velocity is small with $${2\over p}+{3\over q}=2,1 < p \leq \infty$$ . Next, we give ε-regularity criteria in terms of velocity field u and director field Q in Lorentz spaces, which extends the results obtained by Wang et al (J. Evol. Equ. 21: 1627–1650, 2021) for Navier-Stokes equations.