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

By Baoquan Yuan. 2010

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

Subfields: Applied Mathematics, Mathematical Physics

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