Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions

Risk groups for clinical complications of norovirus infections: an outbreak investigation.

Norovirus infections have been described as self-limiting diseases of short duration. An investigation of a norovirus outbreak in a university hospital provided evidence for severe clinical features in patients with several underlying diseases. Clinical outcomes of norovirus infection were defined. Risk-factor analysis targeting underlying diseases and medication was performed using multivariate analyses. In five outbreak wards, 84 patients and 60 nurses were infected (an overall attack rate of 32% in patients, and 76% in nurses). The causative agent was the new variant Grimsby virus. Severe clinical features, including acute renal failure, arrhythmia and signs of acute graft organ rejection in renal transplant patients, were observed in seven (8.3%) patients. In multivariate analyses, cardiovascular disease (OR 17.1, 95% CI 2.17-403) and renal transplant (OR 13.0, 95% CI 1.63-281) were risk-factors for a potassium decrease of >20%. Age >65 years (OR 11.6, 95% CI 1.89-224) was a risk-factor for diarrhoea lasting >2 days. Immunosuppression (OR 5.7, 95% CI 1.78-20.1) was a risk-factor for a creatinine increase of >10%. Norovirus infections in patients with underlying conditions such as cardiovascular disease, renal transplant and immunosuppressive therapy may lead to severe consequences typified by decreased potassium levels, increased levels of C-reactive protein and creatine phosphokinase. In the elderly, norovirus infection may lead to an increased duration of diarrhoea. Therefore patients at risk should be hospitalised early and monitored frequently. Strict preventional measures should be implemented as early as possible to minimise the risk of nosocomial outbreaks

Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and \n u belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.Comment: 10 page

On the existence of traveling waves in the 3D Boussinesq system

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.Comment: 15 pages, to appear in Communications in Mathematical Physic

Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings

A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin orbit and 1PN spin-spin contributions, where the spins are counted of 0PN order.Comment: 26 pages, 1 figure, published in CQG. Current version: we removed a remark and clarified the derivation of the orbital element \e_ph

Entire solutions of hydrodynamical equations with exponential dissipation

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at high wavenumbers $|k|$. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any $C<1/(2\ln 2)$. The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with $C= C_\star =1/\ln2$. The same behavior with a universal constant $C_\star$ is conjectured for the Navier--Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier--Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres

Antecedents and outcomes of consumer environmentally friendly attitudes and behaviour

With the intensification of problems relating to the environment, a growing number of consumers are becoming more ecologically conscious in their preferences and purchases of goods. This paper presents the results of a study conducted among 500 Cypriot consumers, focusing on the factors that shape consumer environmental attitudes and behaviour, as well as on the resulting outcomes. The findings confirmed that both the inward and outward environmental attitudes of a consumer are positively influenced by his/her degree of collectivism, long-term orientation, political involvement, deontology, and law obedience, but have no connection with liberalism. The adoption of an inward environmental attitude was also found to be conducive to green purchasing behaviour that ultimately leads to high product satisfaction. On the other hand, an outward environmental attitude facilitates the adoption of a general environmental behaviour, which is responsible for greater satisfaction with life. The findings of the study have important implications for shaping effective company offerings to consumers in target markets, as well as formulating appropriate policies at the governmental level to enhance environmental sensitivity among citizens

The microbiological quality of air improves when using air conditioning systems in cars

<p>Abstract</p> <p>Background</p> <p>Because of better comfort, air conditioning systems are a common feature in automobiles these days. However, its impact on the number of particles and microorganisms inside the vehicle - and by this its impact on the risk of an allergic reaction - is yet unknown.</p> <p>Methods</p> <p>Over a time period of 30 months, the quality of air was investigated in three different types of cars (VW Passat, VW Polo FSI, Seat Alhambra) that were all equipped with a automatic air conditioning system. Operation modes using fresh air from outside the car as well as circulating air from inside the car were examined. The total number of microorganisms and the number of mold spores were measured by impaction in a high flow air sampler. Particles of 0.5 to 5.0 μm diameter were counted by a laser particle counter device.</p> <p>Results</p> <p>Overall 32 occasions of sampling were performed. The concentration of microorganisms outside the cars was always higher than it was inside the cars. Few minutes after starting the air conditioning system the total number of microorganisms was reduced by 81.7%, the number of mold spores was reduced by 83.3%, and the number of particles was reduced by 87.8%. There were no significant differences neither between the types of cars nor between the types of operation mode of the air conditioning system (fresh air vs. circulating air). All parameters that were looked for in this study improved during utilization of the car's air conditioning system.</p> <p>Conclusions</p> <p>We believe that the risk of an allergic reaction will be reduced during use also. Nevertheless, we recommend regular maintenance of the system and replacement of older filters after defined changing intervals.</p