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

Global exponential stability of classical solutions to the hydrodynamic model for semiconductors

In this paper, the global well-posedness and stability of classical solutions to the multidimensional hydrodynamic model for semiconductors on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve some known results in Sobolev space. The local existence of classical solutions to the Cauchy problem is obtained by the regularized means and compactness argument. Using the high- and low- frequency decomposition method, we prove the global exponential stability of classical solutions (close to equilibrium). Furthermore, it is also shown that the vorticity decays to zero exponentially in the 2D and 3D space. The main analytic tools are the Littlewood-Paley decomposition and Bony's para-product formula.Comment: 18 page

On the global well-posedness for the Boussinesq system with horizontal dissipation

In this paper, we investigate the Cauchy problem for the tridimensional Boussinesq equations with horizontal dissipation. Under the assumption that the initial data is an axisymmetric without swirl, we prove the global well-posedness for this system. In the absence of vertical dissipation, there is no smoothing effect on the vertical derivatives. To make up this shortcoming, we first establish a magic relationship between $\frac{u^{r}}{r}$ and $\frac{\omega_\theta}{r}$ by taking full advantage of the structure of the axisymmetric fluid without swirl and some tricks in harmonic analysis. This together with the structure of the coupling of \eqref{eq1.1} entails the desired regularity.Comment: 32page

On the global well-posedness of a class of Boussinesq- Navier-Stokes systems

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems \partial_{t}u+u\cdot\nabla u+\nabla p+ |D|^{\alpha}u &= \theta e_{2} \partial_{t}\theta+u\cdot\nabla \theta+ |D|^{\beta}\theta &=0 \quad with $\textrm{div} u=0$ and $0<\beta<\alpha<1$. When $\frac{6-\sqrt{6}}{4}<\alpha< 1$, $1-\alpha<\beta\leq f(\alpha)$, where $f(\alpha)$ is an explicit function as a technical bound, we prove global well-posedness results for rough initial data.Comment: 23page

Global classical solutions for partially dissipative hyperbolic system of balance laws

This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of classical solutions in the framework of Chemin-Lerner's spaces with critical regularity is established. To do this, we first explore the functional space theory and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to prove the local well-posedness for general data and global well-posedness for small data by using the Fourier frequency-localization argument. Finally, we apply the new existence theory to a specific fluid model-the compressible Euler equations with damping, and obtain the corresponding results in critical spaces.Comment: 39 page

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

Exploring the equity of GP practice prescribing rates for selected coronary heart disease drugs: a multiple regression analysis with proxies of healthcare need

Background There is a small, but growing body of literature highlighting inequities in GP practice prescribing rates for many drug therapies. The aim of this paper is to further explore the equity of prescribing for five major CHD drug groups and to explain the amount of variation in GP practice prescribing rates that can be explained by a range of healthcare needs indicators (HCNIs). Methods The study involved a cross-sectional secondary analysis in four primary care trusts (PCTs 1–4) in the North West of England, including 132 GP practices. Prescribing rates (average daily quantities per registered patient aged over 35 years) and HCNIs were developed for all GP practices. Analysis was undertaken using multiple linear regression. Results Between 22–25% of the variation in prescribing rates for statins, beta-blockers and bendrofluazide was explained in the multiple regression models. Slightly more variation was explained for ACE inhibitors (31.6%) and considerably more for aspirin (51.2%). Prescribing rates were positively associated with CHD hospital diagnoses and procedures for all drug groups other than ACE inhibitors. The proportion of patients aged 55–74 years was positively related to all prescribing rates other than aspirin, where they were positively related to the proportion of patients aged >75 years. However, prescribing rates for statins and ACE inhibitors were negatively associated with the proportion of patients aged >75 years in addition to the proportion of patients from minority ethnic groups. Prescribing rates for aspirin, bendrofluazide and all CHD drugs combined were negatively associated with deprivation. Conclusion Although around 25–50% of the variation in prescribing rates was explained by HCNIs, this varied markedly between PCTs and drug groups. Prescribing rates were generally characterised by both positive and negative associations with HCNIs, suggesting possible inequities in prescribing rates on the basis of ethnicity, deprivation and the proportion of patients aged over 75 years (for statins and ACE inhibitors, but not for aspirin)

Cytoplasmic and Periplasmic Proteomic Signatures of Exponentially Growing Cells of the Psychrophilic Bacterium Pseudoalteromonas haloplanktis TAC125

peer reviewe

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

The emerging structure of the Extended Evolutionary Synthesis: where does Evo-Devo fit in?

The Extended Evolutionary Synthesis (EES) debate is gaining ground in contemporary evolutionary biology. In parallel, a number of philosophical standpoints have emerged in an attempt to clarify what exactly is represented by the EES. For Massimo Pigliucci, we are in the wake of the newest instantiation of a persisting Kuhnian paradigm; in contrast, Telmo Pievani has contended that the transition to an EES could be best represented as a progressive reformation of a prior Lakatosian scientific research program, with the extension of its Neo-Darwinian core and the addition of a brand-new protective belt of assumptions and auxiliary hypotheses. Here, we argue that those philosophical vantage points are not the only ways to interpret what current proposals to ‘extend’ the Modern Synthesis-derived ‘standard evolutionary theory’ (SET) entail in terms of theoretical change in evolutionary biology. We specifically propose the image of the emergent EES as a vast network of models and interweaved representations that, instantiated in diverse practices, are connected and related in multiple ways. Under that assumption, the EES could be articulated around a paraconsistent network of evolutionary theories (including some elements of the SET), as well as models, practices and representation systems of contemporary evolutionary biology, with edges and nodes that change their position and centrality as a consequence of the co-construction and stabilization of facts and historical discussions revolving around the epistemic goals of this area of the life sciences. We then critically examine the purported structure of the EES—published by Laland and collaborators in 2015—in light of our own network-based proposal. Finally, we consider which epistemic units of Evo-Devo are present or still missing from the EES, in preparation for further analyses of the topic of explanatory integration in this conceptual framework