Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations

In this article, we consider a special class of initial data to the 3D Navier-Stokes equations on the torus, in which there is a certain degree of orthogonality in the components of the initial data. We showed that, under such conditions, the Navier-Stokes equations are globally wellposed. We also showed that there exists large initial data, in the sense of the critical norm $B^{-1}_{\infty,\infty}$ that satisfies the conditions that we considered.Comment: 13 pages, updated references for v

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

Globular clusters and dwarf galaxies in Fornax - I. Kinematics in the cluster core from multi-object spectroscopy

We acquired radial velocities of a significant number of globular clusters (GCs) on wide fields between galaxies in the nearby Fornax cluster of galaxies, in order to derive their velocity dispersion radial profile and to probe the dynamics of the cluster. We used FLAMES on the VLT to obtain accurate velocities for 149 GCs, within a ~500x150 kpc strip centered on NGC 1399, the Fornax central galaxy. These objects are at the very bright tail (M_V < -9.5) of the GC luminosity function, overlapping the so-called ``ultra-compact dwarfs'' magnitude range. Eight of the brightest FLAMES-confirmed members indeed show hints of resolution in the subarcsecond pre-imaging data we used for selecting the ~500 targets for FLAMES spectroscopy. Ignoring the GCs around galaxies by applying 3d_25 diameter masks, we find 61 GCs of 20.0 < V < 22.2 lying in the intra-cluster (IC) medium. The velocity dispersion of the population of ICGCs is 200 km/s at ~150 kpc from the central NGC 1399 and rises to nearly 400 km/s at 200 kpc, a value which compares with the velocity dispersion of the population of dwarf galaxies, thought to be infalling from the surroundings of the cluster.Comment: To be published in A&A Letters. 4 pages, 3 figures, 3 table

Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D

We prove global existence for a nonlinear Smoluchowski equation (a nonlinear Fokker-Planck equation) coupled with Navier-Stokes equations in two dimensions. The proof uses a deteriorating regularity estimate and the tensorial structure of the main nonlinear terms

Extended HI Rotation Curve and Mass Distribution of M31

New HI observations of Messier 31 (M31) obtained with the Effelsberg and Green Bank 100-m telescopes make it possible to measure the rotation curve of that galaxy out to ~35 kpc. Between 20 and 35 kpc, the rotation curve is nearly flat at a velocity of ~226 km/s. A model of the mass distribution shows that at the last observed velocity point, the minimum dark-to-luminous mass ratio is \~0.5 for a total mass of 3.4 10^11 Msol at R < 35 kpc. This can be compared to the estimated MW mass of 4.9 10^11 Msol for R < 50 kpc.Comment: 4 pages, 2 figures, accepted for publication in ApJ Letter

Stellar mass map and dark matter distribution in M31

Stellar mass distribution in M31 is estimated using optical and infrared imaging data. Combining the derived stellar mass model with various kinematical data, properties of the DM halo of the galaxy are constrained. SDSS observations through the ugriz filters and the Spitzer imaging at 3.6 microns are used to sample the SED of the galaxy at each imaging pixel. Intrinsic dust extinction effects are taken into account by using far-infrared observations. Synthetic SEDs created with different stellar population synthesis models are fitted to the observed SEDs, providing estimates for the stellar mass surface density. The stellar mass distribution of the galaxy is described with a 3D model consisting of a nucleus, a bulge, a disc, a young disc and a halo component, each following the Einasto density distribution (relations between different functional forms of the Einasto density distribution are given in App. B). By comparing the stellar mass distribution to the observed rotation curve and kinematics of outer globular clusters and satellite galaxies, the DM halo parameters are estimated. Stellar population synthesis models suggest that M31 is dominated by old stars throughout the galaxy. The total stellar mass is (10-15)10^10Msun, 30% of which is in the bulge and 56% in the disc. None of the tested DM distribution models can be falsified on the basis of the stellar matter distribution and the rotation curve of the galaxy. The virial mass of the DM halo is (0.8-1.1)10^12Msun and the virial radius is 189-213kpc, depending on the DM distribution. The central density of the DM halo is comparable to that of nearby dwarf galaxies, low-surface-brightness galaxies and distant massive disc galaxies, thus the evolution of central DM halo properties seems to be regulated by similar processes for a broad range of halo masses, environments, and cosmological epochs.Comment: 11 pages, 13 figures, 6 tables, accepted for publication in Astronomy and Astrophysic

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