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

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

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

Evidence of ongoing radial migration in NGC 6754: Azimuthal variations of the gas properties

Understanding the nature of spiral structure in disk galaxies is one of the main, and still unsolved questions in galactic astronomy. However, theoretical works are proposing new testable predictions whose detection is becoming feasible with recent development in instrumentation. In particular, streaming motions along spiral arms are expected to induce azimuthal variations in the chemical composition of a galaxy at a given galactic radius. In this letter we analyse the gas content in NGC 6754 with VLT/MUSE data to characterise its 2D chemical composition and H$\alpha$ line-of-sight velocity distribution. We find that the trailing (leading) edge of the NGC 6754 spiral arms show signatures of tangentially-slower, radially-outward (tangentially-faster, radially-inward) streaming motions of metal-rich (poor) gas over a large range of radii. These results show direct evidence of gas radial migration for the first time. We compare our results with the gas behaviour in a $N$-body disk simulation showing spiral morphological features rotating with a similar speed as the gas at every radius, in good agreement with the observed trend. This indicates that the spiral arm features in NGC 6754 may be transient and rotate similarly as the gas does at a large range of radii.Comment: 8 pages, 4 figures, accepted for publication in ApJL 2016 September 2

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

Well-posedness of the Ericksen-Leslie system

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg-Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.Comment: 16 page

Asymmetries in random motions of neutral Hydrogen gas in spiral galaxies

(Abridged). It has been recently shown that random motions of the neutral Hydrogen gas of the Triangulum galaxy (M33) exhibit a bisymmetric perturbation which is aligned with the minor axis of the galaxy, suggesting a projection effect. To investigate if perturbations in the velocity dispersion of nearby discs are comparable to those of M33, the sample is extended to 32 galaxies from The HI Nearby Galaxy Survey and the Westerbork HI Survey of Spiral and Irregular Galaxies. We study velocity asymmetries in the disc planes by performing Fourier transforms of high-resolution HI velocity dispersion maps corrected for beam smearing effects, and measure the amplitudes and phase angles of the Fourier harmonics. We find strong perturbations of first, second and fourth orders. The strongest asymmetry is the bisymmetry, which is predominantly associated with the presence of spiral arms. The first order asymmetry is generally oriented close to the disc major axis, and the second and fourth order asymmetries are preferentially oriented along intermediate directions between the major and minor axes of the discs. These results are evidence that strong projection effects shape the HI velocity dispersion maps. The most likely source of systematic orientations is the anisotropy of velocities, through the projection of streaming motions stronger along one of the planar directions in the discs. Moreover, systematic phase angles of asymmetries in the HI velocity dispersion could arise from tilted velocity ellipsoids. We expect a larger incidence of correlation between the radial and tangential velocities of HI gas. Our methodology is a powerful tool to constrain the dominant direction of streaming motions and thus the shape of the velocity ellipsoid of HI gas, which is de facto anisotropic at the angular scales probed by the observations.Comment: 40 pages, 33 figures. Accepted for publication in Astronomy & Astrophysics. Full resolution version available upon reques

Existence of global strong solutions in critical spaces for barotropic viscous fluids

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\geq2$. We address the question of the global existence of strong solutions for initial data close from a constant state having critical Besov regularity. In a first time, this article show the recent results of \cite{CD} and \cite{CMZ} with a new proof. Our result relies on a new a priori estimate for the velocity, where we introduce a new structure to \textit{kill} the coupling between the density and the velocity as in \cite{H2}. We study so a new variable that we call effective velocity. In a second time we improve the results of \cite{CD} and \cite{CMZ} by adding some regularity on the initial data in particular $\rho_{0}$ is in $H^{1}$. In this case we obtain global strong solutions for a class of large initial data on the density and the velocity which in particular improve the results of D. Hoff in \cite{5H4}. We conclude by generalizing these results for general viscosity coefficients

On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio