We show—in the framework of physical scales and (K1, K2)-averages— that Kolmogorov’s dissipation law combined with the smallness condition on a Taylor length scale is sufficient to guarantee energy cascades in the forced Navier–Stokes equations. Moreover, in the periodic case we establish restrictive scaling laws—in terms of Grashof number—for kinetic energy, energy flux, and energy dissipation...

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, ...

In this Letter we extend the heuristic discussion of [1] to a Schwarzschildde Sitter spacetime (SdS), based on the generalized uncertainty principle(GUP). We try to explain the present value of the vacuum energy density. An inequality is put forward as an explanation for the smallness of the cosmological constant, and the relationship between the Bekenstein and the Bekenstein-Hawking entropy bo...

We find all possible seesaw textures which can describe in a natural way the currently observed neutrino oscillation pattern in terms of a minimum number of parameters. Natural here means due only to the relative smallness (vanishing) of some parameters in the relevant lagrangian, without special relations or accidental cancellations among them. The corresponding predictions for the mixing angl...

Fetal growth restriction (FGR) diagnosed before 32 weeks is identified by fetal smallness associated with Doppler abnormalities and is associated with significant perinatal morbidity and mortality and maternal complications. Recent studies have provided new insights into pathophysiology, management options and postnatal outcomes of FGR. In this paper we review the available evidence regarding d...

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a...

We prove the global existence of weak solutions of the Cauchy problem for the Navier-Stokes equations of compressible, isentropic flow of a polytropic gas in one space dimension. The initial velocity and density are assumed to be in L2 and L2 n BV respectively, modulo additive constants. In particular, no smallness assumptions are made about the intial data. In addition, we prove a result conce...

We prove the existence and uniqueness of global strong solutions to the one dimensional, compressible Navier-Stokes system for the viscous and heat conducting ideal polytropic gas flow, when heat conductivity depends on temperature in power law of Chapman-Enskog. The results reported in this article is valid for initial boundary value problem with non-slip and heat insulated boundary along with...

The present paper is dedicated to the study of the global existence for the inviscid two-dimensional Boussinesq system. We focus on finite energy data with bounded vorticity and we find out that, under quite a natural additional assumption on the initial temperature, there exists a global unique solution. None smallness conditions are imposed on the data. The global existence issues for infinit...

We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric standard model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultraviolet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative correcti...