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This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in R3{{\mathbb{R}}}^{3}, which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the Lp{L}^{p}-in-time and Lq{L}^{q}-in-space setting with (p,q)∈(2,∞)×(3,∞)\left(p,q)\in \left(2,\infty )\times \left(3,\infty ) satisfying 2/p+3/q

Let Ω be an exterior Lipschitz domain in R². It is proved that the Helmholtz decomposition of the vector fields in Lp(Ω; R²) exists if p satisfies |1/p−1/2| < 1/4+ε with some constant ε = ε(Ω) ∈ (0, 1/4], where it is allowed to take ε = 1/4 if ∂Ω ∈ C¹. [ABSTRACT FROM AUTHOR]

Consider the chemotaxis–Navier–Stokes equations on a bounded convex domain Ω ⊂ R 3 , where the boundary ∂ Ω of Ω is not necessarily smooth. It is shown that this system admits a unique strong 2 π -periodic solution provided that given 2 π -periodic forcing functions are sufficiently small in their natural norm. The result may extend to general cases Ω ⊂ R d , d ≥ 2 , if one additionally assumes that ∂ Ω is of class C 3. The nonnegativity of solutions is also discussed. [ABSTRACT FROM AUTHOR]

We investigate a class of functionals on Möbius gyrovector spaces, which consists of a counterpart to bounded linear functionals on Hilbert spaces. [ABSTRACT FROM AUTHOR]

We investigated changes in starch content and starch metabolic enzyme activities in developing and postharvest squash of distinct species, Cucurbita maxima and Cucurbita moschata, which accumulate high and low levels of starch, respectively. The total activity of starch phosphorylase in developing fruits significantly correlated (r = 0.99) to the amount of starch among Cucurbita species (C. maxima, C. moschata and C. pepo). Separable activity of a plastidial L‐form phosphorylase in C. maxima fruit markedly increased corresponding with starch accumulation. We isolated two genes (CmPhoL1 and CmPhoH1) encoding an L‐form and a cytosolic H‐form phosphorylase from C. maxima fruit. The expression of CmPhoL1 in the fruit dramatically increased at the beginning of starch accumulation. Recombinant CmPhoL1 enzyme showed similar kinetic parameters in both glucan synthesis and phosphorolysis: this enzyme can catalyze the invertible reaction in vitro depending on the concentration of substrates. These results suggest that CmPhoL1 plays a role in the starch accumulation process during squash development, but the aid of other starch synthetic enzymes may be required for in vivo glucan synthesis reaction by CmPhoL1. An importance of plastidial starch phosphorylase in the starch accumulation in the fruit organ was indicated. [ABSTRACT FROM AUTHOR]