On the regularity criteria of weak solutions to the micropolar fluid equations in Lorentz space

Original · EN

In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space Lᵖ,∞(R³). We obtain that if u∈ Lq(0,T;Lᵖ,∞(R³)) for 2q+3p≤ 1 with 3<p≤ ∞; or ∇ u∈ Lq(0,T;Lᵖ,∞(R³)) for 2q+3p≤ 2 with 32<p≤ ∞; or the pressure P∈ Lq(0,T;Lᵖ,∞(R³)) for 2q+3p≤ 2 with 32<p≤ ∞; or ∇ P∈ Lq(0,T;Lᵖ,∞(R³)) for 2q+3p≤ 3 with 1<p≤ ∞, then the weak solution (u,ω) satisfying the energy inequality is a smooth solution on [0,T).