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This paper develops L p - L q decay estimates of the gradient of the Stokes semigroup (T (t)) t ≥ 0 generated by the negative of the Stokes operator in exterior Lipschitz domains Ω ⊂ R n , n ≥ 3. More precisely, the L p - L q estimates of ∇ T (t) with optimal rates are proved if p and q satisfy | 1 / p − 1 / 2 | < 1 / (2 n) + ε , | 1 / q − 1 / 2 | < 1 / (2 n) + ε , and p ≤ q ≤ n with some ε > 0 , which should be useful for the study of stability of the several physically relevant flows. As an application, we obtain the existence theorem of global-in-time strong solutions to the three-dimensional Navier–Stokes equations in the critical space L ∞ (0 , ∞ ; L σ 3 (Ω)) provided that the initial velocity is small in the L 3 -norm. [ABSTRACT FROM AUTHOR]

We show that the Stokes operator defined on L σ p (Ω) for an exterior Lipschitz domain Ω ⊂ R n (n ≥ 3) admits maximal regularity provided that p satisfies | 1 / p − 1 / 2 | < 1 / (2 n) + ε for some ε > 0. In particular, we prove that the negative of the Stokes operator generates a bounded analytic semigroup on L σ p (Ω) for such p. In addition, L p - L q -mapping properties of the Stokes semigroup and its gradient with optimal decay estimates are obtained. This enables us to prove the existence of mild solutions to the Navier–Stokes equations in the critical space L ∞ (0 , T ; L σ 3 (Ω)) (locally in time and globally in time for small initial data). [ABSTRACT FROM AUTHOR]

In this study, we show that any finitely generated gyrovector subspace in the Möbius gyrovector space coincides with the intersection of the vector subspace generated by the same generators and the Möbius ball. As an application, we present a notion of orthogonal gyrodecomposition and clarify the relationship with the orthogonal decomposition. [ABSTRACT FROM AUTHOR]

To investigate how the conformational flexibility of subtilisin affects its ability to discriminate between enantiomeric amino acid and ester substrates for the subtilisin-catalyzed reaction in an organic solvent, the flexibility around the active site and the surface of subtilisin was estimated from the mobility of a spin label bound to subtilisin by ESR spectroscopy. Many studies on enzyme flexibility focus on the active site. Both the surface and active site flexibility play an important role in the enantioselectivity enhancement of the enzyme-catalyzed reaction. It was found, however, that the different behavior observed for the enantioselectivity between the amino acid and ester substrates could be correlated with the flexibility around the surface rather than the flexibility at the active site of subtilisin. In other words, for the ester substrates, the greater flexibility around the surface of subtilisin induced by a conformational change resulting from the presence of an additive such as DMSO is essential for the enantioselectivity enhancement. This model is also supported by the Michaelis–Menten kinetic parameters for each enantiomeric substrate. Our findings provide insight into the enantioselectivity enhancement for the resolution of enantiomers for enzyme-catalyzed reactions in organic solvents. [Copyright &y& Elsevier]