Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index s=−1s=-1

This paper is concerned with well-posedness of the Boussinesq system. We prove that the $n$ ($n\ge2$) dimensional Boussinesq system is well-psoed for small initial data $(\vec{u}_0,\theta_0)$ ($\nabla\cdot\vec{u}_0=0$) either in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times{B}^{-1}_{p,r}$ or in ${B^{-1,1}_{\infty,\infty}}\times{B}^{-1,\epsilon}_{p,\infty}$ if $r\in[1,\infty]$, $\epsilon>0$ and $p\in(\frac{n}{2},\infty)$, where $B^{s,\epsilon}_{p,q}$ ($s\in\mathbb{R}$, $1\leq p,q\leq\infty$, $\epsilon>0$) is the logarithmically modified Besov space to the standard Besov space $B^{s}_{p,q}$. We also prove that this system is well-posed for small initial data in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times({B}^{-1}_{\frac{n}{2},1}\cap{B^{-1,1}_{\frac{n}{2},\infty}})$.Comment: 18 page

Existence of global strong solutions in critical spaces for barotropic viscous fluids

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\geq2$. We address the question of the global existence of strong solutions for initial data close from a constant state having critical Besov regularity. In a first time, this article show the recent results of \cite{CD} and \cite{CMZ} with a new proof. Our result relies on a new a priori estimate for the velocity, where we introduce a new structure to \textit{kill} the coupling between the density and the velocity as in \cite{H2}. We study so a new variable that we call effective velocity. In a second time we improve the results of \cite{CD} and \cite{CMZ} by adding some regularity on the initial data in particular $\rho_{0}$ is in $H^{1}$. In this case we obtain global strong solutions for a class of large initial data on the density and the velocity which in particular improve the results of D. Hoff in \cite{5H4}. We conclude by generalizing these results for general viscosity coefficients

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur

Association Between Clinical Pathways Leading to Medical Management and Prognosis in Patients With NSTEACS.

: A large proportion of patients with non-ST-segment elevation acute coronary syndrome (NSTEACS) are initially selected for medical management (MM) and do not undergo coronary revascularization during or immediately after the index event. The aim of this study was to explore the clinical pathways leading to MM in NSTEACS patients and their influence on prognosis. : Patient characteristics, pathways leading to MM, and 2-year outcomes were recorded in a prospective cohort of 5591 NSTEACS patients enrolled in 555 hospitals in 20 countries across Europe and Latin America. Cox models were used to assess the impact of hospital management on postdischarge mortality. : Medical management was the selected strategy in 2306 (41.2%) patients, of whom 669 (29%) had significant coronary artery disease (CAD), 451 (19.6%) had nonsignificant disease, and 1186 (51.4%) did not undergo coronary angiography. Medically managed patients were older and had higher risk features than revascularized patients. Two-year mortality was higher in medically managed patients than in revascularized patients (11.0% vs 4.4%; P &lt; .001), with higher mortality rates in patients who did not undergo angiography (14.6%) and in those with significant CAD (9.3%). Risk-adjusted mortality was highest for patients who did not undergo angiography (HR = 1.81; 95%CI, 1.23-2.65), or were not revascularized in the presence of significant CAD (HR = 1.90; 95%CI, 1.23-2.95) compared with revascularized patients. : Medically managed NSTEACS patients represent a heterogeneous population with distinct risk profiles and outcomes. These differences should be considered when designing future studies in this population.<br/

Evidence that pairing with genetically similar mates is maladaptive in a monogamous bird

<p>Abstract</p> <p>Background</p> <p>Evidence of multiple genetic criteria of mate choice is accumulating in numerous taxa. In many species, females have been shown to pair with genetically dissimilar mates or with extra-pair partners that are more genetically compatible than their social mates, thereby increasing their offsprings' heterozygosity which often correlates with offspring fitness. While most studies have focused on genetically promiscuous species, few studies have addressed genetically monogamous species, in which mate choice tends to be mutual.</p> <p>Results</p> <p>Here, we used microsatellite markers to assess individual global heterozygosity and genetic similarity of pairs in a socially and genetically monogamous seabird, the black-legged kittiwake <it>Rissa tridactyla</it>. We found that pairs were more genetically dissimilar than expected by chance. We also identified fitness costs of breeding with genetically similar partners: (i) genetic similarity of pairs was negatively correlated with the number of chicks hatched, and (ii) offspring heterozygosity was positively correlated with growth rate and survival.</p> <p>Conclusion</p> <p>These findings provide evidence that breeders in a genetically monogamous species may avoid the fitness costs of reproducing with a genetically similar mate. In such species that lack the opportunity to obtain extra-pair fertilizations, mate choice may therefore be under high selective pressure.</p

The sharp-interface limit for the Navier--Stokes--Korteweg equations

We investigate the sharp-interface limit for the Navier--Stokes--Korteweg model, which is an extension of the compressible Navier--Stokes equations. By means of compactness arguments, we show that solutions of the Navier--Stokes--Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions

Persistence and transmission of tick-borne viruses: Ixodes ricinus and louping-ill virus in red grouse populations

The population dynamics of tick-borne disease agents and in particular the mechanisms which influence their persistence are examined with reference to the flavivirus that causes louping-ill in red grouse and sheep. Pockets of infection cause heavy mortality and the infection probably persists as a consequence of immigration of susceptible hosts. Seroprevalence is positively associated with temporal variations in vectors per host, although variation between areas is associated with the abundance of mountain hares. The presence of alternative tick hosts, particularly large mammals, provides additional hosts for increasing tick abundance. Grouse alone can not support the vectors and the pathogen but both can persist when a non-viraemic mammalian host supports the tick population and a sufficiently high number of nymphs bite grouse. These alternative hosts may also amplify virus through non-viraemic transmission by the process of co-feeding, although the relative significance of this has yet to be determined. Another possible route of infection is through the ingestion of vectors when feeding or preening. Trans-ovarial transmission is a potentially important mechanism for virus persistence but has not been recorded with louping-ill and ixodes ricinus. The influence of non-viraemic hosts, both in the multiplication of vectors and the amplification of virus through non-viraemic transmission are considered significant for virus persistence

A cost-effectiveness analysis of the management of sore throat in children in Australia

For the first time a cost-effectiveness analysis of the management of sore throat in Australian children has been conducted using accurate epidemiological data generated from recent Australian studies.<br /

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.Comment: To appear in "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final publication is available at http://www.springerlink.co