Logarithmical Blow-up Criteria for the Nematic Liquid Crystal Flows

الأصل · EN

We investigate the blow-up criterion for the local in time classical solution of the nematic liquid crystal flows in dimension two and three. More precisely, 0<T*<+∞ is the maximal time interval if and only if (i) for n=3, align* ∫₀ᵗ*ωB⁰∞,∞+∇ dB⁰∞,∞²√1+ln(e+ωB⁰∞,∞ +∇ dB⁰∞,∞)dt=∞, align* or align* ∫₀ᵗ*∇ uB⁻¹∞,∞²+∇ dB⁰∞,∞²√1+ln(e+∇ uB⁻¹∞,∞ +∇ dB⁰∞,∞)dt=∞; align* and (ii) for n=2, align* ∫₀ᵗ*∇ dB⁰∞,∞²√1+ln(e +∇ dB⁰∞,∞)dt=∞. align*