Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Horizontal Eddy Diffusivity

In this paper, we consider the initial-boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation. Global well-posedness of strong solutions are established with $H^2$ initial data.Comment: arXiv admin note: substantial text overlap with arXiv:1312.603

A mathematical model for mechanotransduction at the early steps of suture formation

Growth and patterning of craniofacial sutures are subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron x-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (\emph{Polypterus bichir}) and a placoderm (\emph{Compagopiscis croucheri}), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion

Existence of weak solution for compressible fluid models of Korteweg type

This work is devoted to prove existence of global weak solutions for a general isothermal model of capillary fluids derived by J.- E Dunn and J. Serrin (1985) [6], which can be used as a phase transition model. We improve the results of [5] by showing the existence of global weak solution in dimension two for initial data in the energy space, close to a stable equilibrium and with specific choices on the capillary coefficients. In particular we are interested in capillary coefficients approximating a constant capillarity coefficient. To finish we show the existence of global weak solution in dimension one for a specific type of capillary coefficients with large initial data in the energy space

Weak solutions to problems involving inviscid fluids

We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method of convex integration we show the existence of infinitely many weak solutions for prescribed initial data and kinetic energy

A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions

Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Simplifying the flow we turn to consider a 2-dimensional Poisson problem that conserves essential features related to the rough boundary. Then, we investigate convergence of boundary layer approximations and the corresponding wall laws in the case of Neumann type boundary conditions at the inlet and outlet parts of the domain. The difficulty comes from the fact that correctors, for the boundary layers near the rough surface, may introduce error terms on the other portions of the boundary. In order to correct these spurious oscillations, we introduce a vertical boundary layer. Trough a careful study of its behavior, we prove rigorously decay estimates. We then construct complete boundary layers that respect the macroscopic boundary conditions. We also derive error estimates in terms of the roughness size epsilon either for the full boundary layer approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda

Projected impact of heat on mortality and labour productivity under climate change in Switzerland

Extreme temperatures have reached unprecedented levels in many regions of the globe due to climate change, and a further increase is expected. Besides other consequences, high temperatures increase the mortality risk and severely affect the labour productivity of workers. We perform a high-resolution spatial analysis to assess the impacts of heat on mortality and labour productivity in Switzerland and project their development under different Representative Concentration Pathway (RCP) scenarios, considering that no socio-economic changes take place. The model is based on the risk framework of the Intergovernmental Panel on Climate Change (IPCC), which combines the three risk components: hazard, exposure, and vulnerability. We model the two impact categories in the same spatially explicit framework, and we integrate uncertainties into the analysis by a Monte Carlo simulation. We model first that about 658 deaths are associated with heat exposure currently each year in Switzerland. Second, the economic costs caused by losses in labour productivity amount to around CHF 665 million (approx. USD 700 million) per year. Should we remain on an RCP8.5 emissions pathway, these values may double (for mortality) or even triple (for labour productivity) by the end of the century. Under an RCP2.6 scenario impacts are expected to slightly increase and peak around mid-century, when climate is assumed to stop warming. Even though uncertainties in the model are large, the underlying trend in impacts is unequivocal. The results of the study are valuable information for political discussions and allow for a better understanding of the cost of inaction

Drought-induced building damages from simulations at regional scale

We present a model computing damage costs from drought-induced soil subsidence related to shrinking and swelling soils. The model uses an indicator applicable across different climate regimes. The influence of geology and land use on regional damage levels is taken into account. Simulation results are evaluated at departmental scale, showing a good representation of the regions affected by drought-induced soil subsidence. Substantial differences between simulated and observed damages are however found in some departments

Customising global climate science for national adaptation: A case study of climate projections in UNFCCC’s National Communications

Countries differ markedly in their production of climate science. While richer nations are often home to a variety of climate models, data infrastructures and climate experts, poorer sovereigns often lack these attributes. However, less is known about countries’ capacity to use global climate science and customise it into products informing national adaptation. We use a unique global dataset, the UNFCCC National Communications, to perform a global documentary analysis of scientific submissions from individual countries (n = 189). Comparing countries’ climate projections with their competence in publishing climate science, our research examines the existence of geographical divides. Although countries proficient in publishing climate science use more complex climate modelling techniques, key characteristics of climate projections are highly similar around the globe, including multi-model ensembles of Global Circulation Models (GCMs). This surprising result is made possible because of the use of pre-configured climate modelling software packages. One concern is that these tools restrict customisation, such as country-specific observations, modelling information, and visualisation. Such tools may therefore hide a new geographical divide where countries with higher scientific capacities are able to inform what goes into these software packages, whereas lower scientific capacity countries are dependent upon these choices – whether beneficial for them or not. Our research suggests that free-to-use modelling and training efforts may unwittingly restrict, rather than foster, countries’ capacity to customise global climate science into nationally relevant and legitimate climate information