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

Animal vulnerability and the necessity of protecting them

In Romania, there are at least 14 animal species represented by 123 animal breeds and pure lines listed on the List of animal genetic resources in critical state, threatened, or vulnerable. Though these animal species need to be protected, their conservation has not been supported financially. These categories of vulnerable animals are represented by: 13 sheep breeds, 19 fish species and breeds, 2 goat breeds, 2 swine breeds, 4 goose breeds, 61 chicken breeds and pure lines, 7 turkey populations, 7 duck breeds, the Romanian buffalo, and a bovine breed, the Sură de stepă

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

Animal vulnerability and the necessity of protecting them

In Romania, there are at least 14 animal species represented by 123 animal breeds and pure lines listed on the List of animal genetic resources in critical state, threatened, or vulnerable. Though these animal species need to be protected, their conservation has not been supported financially. These categories of vulnerable animals are represented by: 13 sheep breeds, 19 fish species and breeds, 2 goat breeds, 2 swine breeds, 4 goose breeds, 61 chicken breeds and pure lines, 7 turkey populations, 7 duck breeds, the Romanian buffalo, and a bovine breed, the Sură de stepă

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