Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces

This paper is devoted to the study of the Cauchy problem for the Boussinesq system with partial viscosity in dimension $N\geq3.$ First we prove a global existence result for data in Lorentz spaces satisfying a smallness condition which is at the scaling of the equations. Second, we get a uniqueness result in Besov spaces with {\it negative} indices of regularity (despite the fact that there is no smoothing effect on the temperature). The proof relies on a priori estimates with loss of regularity for the nonstationary Stokes system with convection. As a corollary, we obtain a global existence and uniqueness result for small data in Lorentz spaces.Comment: 24 pages. Physica D, in pres

On the hydrostatic approximation of the Navier-Stokes equations in a thin strip

In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes system with analytic data

Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces, $B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$. Then, we prove the global wellposedness for (\textit{ANS}) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In particular, our results imply the global wellposedness of (\textit{ANS}) with high oscillatory initial data.Comment: 39 page

The Leray and Fujita-Kato theorems for the Boussinesq system with partial viscosity

We are concerned with the so-called Boussinesq equations with partial viscosity. These equations consist of the ordinary incompressible Navier-Stokes equations with a forcing term which is transported {\it with no dissipation} by the velocity field. Such equations are simplified models for geophysics (in which case the forcing term is proportional either to the temperature, or to the salinity or to the density). In the present paper, we show that the standard theorems for incompressible Navier-Stokes equations may be extended to Boussinesq system despite the fact that there is no dissipation or decay at large time for the forcing term. More precisely, we state the global existence of finite energy weak solutions in any dimension, and global well-posedness in dimension $N\geq3$ for small data. In the two-dimensional case, the finite energy global solutions are shown to be unique for any data in $L^2(\R^2).$Comment: Bulletin de la Societe Mathematique de France, in pres

Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data

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 infinite energy initial velocity, and for the B\'enard system are also discussed.Comment: 12 page

Uniform Local Existence for Inhomogeneous Rotating Fluid Equations

We investigate the equations of anisotropic incompressible viscous fluids in $\R^3$, rotating around an inhomogeneous vector $B(t, x_1, x_2)$. We prove the global existence of strong solutions in suitable anisotropic Sobolev spaces for small initial data, as well as uniformlocal existence result with respect to the Rossby number in the same functional spaces under the additional assumption that $B=B(t,x_1)$ or $B=B(t,x_2)$. We also obtain the propagation of the isotropic Sobolev regularity using a new refined product law.Comment: 25 pages, to appear in Journal of Dynamics and Differential Equation

Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System

We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak solutions in dimensions two and three. We show the existence of a Lyapunov functional for the smooth solutions of the coupled system and use the cancellations that allow its existence to prove higher global regularity, in dimension two. We also show the weak-strong uniqueness in dimension two

Probing Tectonic Topography in the Aftermath of Continental Convergence in Central Europe

Continental topography is at the interface of processes taking place at depth in the Earth,at its surface,and above it.Topography influences society, not only in terms of slow processes of landscape change and earthquakes,but also in terms of how it affects climate.The Pannonian Basin–Carpathian Orogen System in Central and Eastern Europe represents a key natural laboratory for the development of a new generation of models for ongoing orogeny and its effect on continental topography development (Figure 1).This system comprises some of the best documented sedimentary basins in the world,located within the Alpine orogenic belt, at the transition between the western European lithosphere and the East European Craton. It includes one of the most active seismic zones in Europe,with intermediate depth (50–220 km) mantle earthquakes of significant magnitude occurring in a geographically restricted area in the Vrancea zone of southeastern Romania

The evolutionary dynamics of microRNAs in domestic mammals

MiRNAs are crucial regulators of gene expression found across both the plant and animal kingdoms. While the number of annotated miRNAs deposited in miRBase has greatly increased in recent years, few studies provided comparative analyses across sets of related species, or investigated the role of miRNAs in the evolution of gene regulation. We generated small RNA libraries across 5 mammalian species (cow, dog, horse, pig and rabbit) from 4 different tissues (brain, heart, kidney and testis). We identified 1676 miRBase and 413 novel miRNAs by manually curating the set of computational predictions obtained from miRCat and miRDeep2. Our dataset spanning five species has enabled us to investigate the molecular mechanisms and selective pressures driving the evolution of miRNAs in mammals. We highlight the important contributions of intronic sequences (366 orthogroups), duplication events (135 orthogroups) and repetitive elements (37 orthogroups) in the emergence of new miRNA loci. We use this framework to estimate the patterns of gains and losses across the phylogeny, and observe high levels of miRNA turnover. Additionally, the identification of lineage-specific losses enables the characterisation of the selective constraints acting on the associated target sites. Compared to the miRBase subset, novel miRNAs tend to be more tissue specific. 20 percent of novel orthogroups are restricted to the brain, and their target repertoires appear to be enriched for neuron activity and differentiation processes. These findings may reflect an important role for young miRNAs in the evolution of brain expression plasticity. Many seed sequences appear to be specific to either the cow or the dog. Analyses on the associated targets highlight the presence of several genes under artificial positive selection, suggesting an involvement of these miRNAs in the domestication process. Altogether, we provide an overview on the evolutionary mechanisms responsible for miRNA turnover in 5 domestic species, and their possible contribution to the evolution of gene regulation