[再寄小读者之数学篇](2014-06-26 Logarithmical Sobolev inequality using BMO space)

$$ex q>3 a sen{ f}_{L^infty} leq C(q)sez{ 1+sen{ f}_{BMO} ln^frac{1}{2}sex{e+sen{ f}_{W^{1,q}}+sen{f}_{L^infty}} }. eex$$ $$ex mgeq 3 a sen{ f}_{L^infty}leq Csez{ 1+sen{ f}_{BMO} ln^frac{1}{2} sex{1+sen{ f}_{H^m}} }. eex$$  see [D. Chae, J. Lee, On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics, J. Differential Equations, 256 (2014), 3835--3858].