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

Generalized momenta of mass and their applications to the flow of compressible fluid

We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of the solutions with uniform deformation and the study of behavior of the boundary of a material volume of liquid.Comment: 10 pages, Proceedings of the International Conference on Hyperbolic Problems, Lyon, 2006, France. In pres

Modeling Non-Circular Motions in Disk Galaxies: Application to NGC 2976

We present a new procedure to fit non-axisymmetric flow patterns to 2-D velocity maps of spiral galaxies. We concentrate on flows caused by bar-like or oval distortions to the total potential that may arise either from a non-axially symmetric halo or a bar in the luminous disk. We apply our method to high-quality CO and Halpha data for the nearby, low-mass spiral NGC 2976 previously obtained by Simon et al., and find that a bar-like model fits the data at least as well as their model with large radial flows. We find supporting evidence for the existence of a bar in the baryonic disk. Our model suggests that the azimuthally averaged central attraction in the inner part of this galaxy is larger than estimated by these authors. It is likely that the disk is also more massive, which will limit the increase to the allowed dark halo density. Allowance for bar-like distortions in other galaxies may either increase or decrease the estimated central attraction.Comment: 12 pages, 6 figures, accepted for publication in ApJ. v2: minor changes to match proofs. For version with high-resolution figures, see http://www.physics.rutgers.edu/~spekkens/papers/noncirc.pd

HI studies of the Sculptor group galaxies. VIII. The background galaxies: NGC 24 and NGC 45

In order to complete our HI survey of galaxies in the Sculptor group area, VLA observations of NGC 24 and NGC 45 are presented. These two galaxies of similar magnitude M_B ~ -17.4 lie in the background of the Sculptor group and are low surface brightness galaxies, especially NGC 45. The HI distribution and kinematics are regular for NGC 24 while NGC 45 exhibits a kinematical twist of its major axis. A tilted-ring model shows that the position angle of the major axis changes by ~25 degrees. A best-fit model of their mass distribution gives mass-to-light ratios for the stellar disk of 2.5 and 5.2 for NGC 24 and NGC 45 respectively. These values are higher than the ones expected from stellar population synthesis models. Despite the large dark matter contribution, the galaxy mass is still dominated by the stellar component in their very inner regions. These high mass-to-light ratios are typical of what is seen in low surface brightness galaxies and may indicate that, in those galaxies, disks are far from the maximum disk case. The halo parameters derived from the best-fit models are thus lower limits.Comment: 23 pages, 10 figures, accepted for publication in The Astronomical Journa

On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces

In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, we fill a gap in a step of the proof of the local well-posedness part for the incompressible Euler equation in \cite{Chae1}.Comment: 16page

Ram pressure stripping of the multiphase ISM in the Virgo cluster spiral galaxy NGC 4438

Ram pressure stripping of the multiphase ISM is studied in the perturbed Virgo cluster spiral galaxy NGC 4438. This galaxy underwent a tidal interaction ~100 Myr ago and is now strongly affected by ram pressure stripping. Deep VLA radio continuum observations at 6 and 20 cm are presented. We detect prominent extraplanar emission to the west of the galactic center, which extends twice as far as the other tracers of extraplanar material. The spectral index of the extraplanar emission does not steepen with increasing distance from the galaxy. This implies in situ re-acceleration of relativistic electrons. The comparison with multiwavelength observations shows that the magnetic field and the warm ionized interstellar medium traced by Halpha emission are closely linked. The kinematics of the northern extraplanar Halpha emission, which is ascribed to star formation, follow those of the extraplanar CO emission. In the western and southern extraplanar regions, the Halpha measured velocities are greater than those of the CO lines. We suggest that the ionized gas of this region is excited by ram pressure. The spatial and velocity offsets are consistent with a scenario where the diffuse ionized gas is more efficiently pushed by ram pressure stripping than the neutral gas. We suggest that the recently found radio-deficient regions compared to 24 mum emission are due to this difference in stripping efficiency.Comment: 8 pages, 6 figures, A&A, accepted for publicatio

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

The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, i. e. \sup_{j\in\Z}\int_0^T\|\Delta_j(\na\times u)\|_\infty dt, where $\Delta_j$ is a frequency localization on $|\xi|\approx 2^j$.Comment: 12page

The catalog of radial velocity standard stars for the Gaia RVS: status and progress of the observations

A new full-sky catalog of Radial Velocity standard stars is being built for the determination of the Radial Velocity Zero Point of the RVS on board of Gaia. After a careful selection of 1420 candidates matching well defined criteria, we are now observing all of them to verify that they are stable enough over several years to be qualified as reference stars. We present the status of this long-term observing programme on three spectrographs : SOPHIE, NARVAL and CORALIE, complemented by the ELODIE and HARPS archives. Because each instrument has its own zero-point, we observe intensively IAU RV standards and asteroids to homogenize the radial velocity measurements. We can already estimate that ~8% of the candidates have to be rejected because of variations larger than the requested level of 300 m/s.Comment: Proceedings of SF2A2010, S. Boissier, M. Heydari-Malayeri, R. Samadi and D. Valls-Gabaud (eds), 3 pages, 2 figure