The galaxy halo formation in the absence of violent relaxation and a universal density profile of the halo center

While N-body simulations testify for a cuspy profile of the central region of the dark matter haloes, observations favor a shallow, cored density profile of the central region of, at least, some spiral galaxies and dwarf spheroidals. We show that a central profile, very close to the observed one, inevitably forms in the center of dark matter haloes if we make a supposition about a moderate energy relaxation of the system during the halo formation. If we assume the energy exchange between dark matter particles during the halo collapse to be not too intensive, the profile is universal: it depends almost not at all on the properties of the initial perturbation and is very akin, but not identical, to the Einasto profile with small Einasto index $n\sim 0.5$. We estimate the size of the 'central core' of the distribution, i.e., the extent of the very central region with a respectively gentle profile, and show that the cusp formation is unlikely, even if the dark matter is cold. The obtained profile is in a good agreement with observational data for, at least, some types of galaxies, but clearly disagrees with N-body simulations.Comment: 8 pages, 4 figure

On the global well-posedness of a class of Boussinesq- Navier-Stokes systems

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems \partial_{t}u+u\cdot\nabla u+\nabla p+ |D|^{\alpha}u &= \theta e_{2} \partial_{t}\theta+u\cdot\nabla \theta+ |D|^{\beta}\theta &=0 \quad with $\textrm{div} u=0$ and $0<\beta<\alpha<1$. When $\frac{6-\sqrt{6}}{4}<\alpha< 1$, $1-\alpha<\beta\leq f(\alpha)$, where $f(\alpha)$ is an explicit function as a technical bound, we prove global well-posedness results for rough initial data.Comment: 23page

Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde

WKB analysis for nonlinear Schr\"{o}dinger equations with potential

We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity.Comment: 25 pages, 11pt, a4. Appendix withdrawn, due to some inconsistencie

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

Physical conditions in the ISM of intensely star-forming galaxies at redshift~2

We analyze the physical conditions in the interstellar gas of 11 actively star-forming galaxies at z~2, based on integral-field spectroscopy from the ESO-VLT and HST/NICMOS imaging. We concentrate on the high H-alpha surface brightnesses, large line widths, line ratios and the clumpy nature of these galaxies. We show that photoionization calculations and emission line diagnostics imply gas pressures and densities that are similar to the most intense nearby star-forming regions at z=0 but over much larger scales (10-20 kpc). A relationship between surface brightness and velocity dispersion can be explained through simple energy injection arguments and a scaling set by nearby galaxies with no free parameters. The high velocity dispersions are a natural consequence of intense star formation thus regions of high velocity dispersion are not evidence for mass concentrations such as bulges or rings. External mechanisms like cosmological gas accretion generally do not have enough energy to sustain the high velocity dispersions. In some cases, the high pressures and low gas metallicites may make it difficult to robustly distinguish between AGN ionization cones and star formation, as we show for BzK-15504 at z=2.38. We construct a picture where the early stages of galaxy evolution are driven by self-gravity which powers strong turbulence until the velocity dispersion is high. Then massive, dense, gas-rich clumps collapse, triggering star formation with high efficiencies and intensities as observed. At this stage, the intense star formation is likely self-regulated by the mechanical energy output of massive stars.Comment: ApJ accepted main journal, 21 pages, 12 figure

Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress

We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial diffusion of the polymeric stresses

The Triangulum Extended (TREX) Survey: The Stellar Disk Dynamics of M33 as a Function of Stellar Age

Triangulum, M33, is a low mass, relatively undisturbed spiral galaxy that offers a new regime in which to test models of dynamical heating. In spite of its proximity, the dynamical heating history of M33 has not yet been well constrained. In this work, we present the TREX Survey, the largest stellar spectroscopic survey across the disk of M33. We present the stellar disk kinematics as a function of age to study the past and ongoing dynamical heating of M33. We measure line of sight velocities for ~4,500 disk stars. Using a subset, we divide the stars into broad age bins using Hubble Space Telescope and Canada-France-Hawaii-Telescope photometric catalogs: massive main sequence stars and helium burning stars (~80 Myr), intermediate mass asymptotic branch stars (~1 Gyr), and low mass red giant branch stars (~4 Gyr). We compare the stellar disk dynamics to that of the gas using existing HI, CO, and Halpha kinematics. We find that the disk of M33 has relatively low velocity dispersion (~16 km/s), and unlike in the Milky Way and Andromeda galaxies, there is no strong trend in velocity dispersion as a function of stellar age. The youngest disk stars are as dynamically hot as the oldest disk stars and are dynamically hotter than predicted by most M33 like low mass simulated analogs in Illustris. The velocity dispersion of the young stars is highly structured, with the large velocity dispersion fairly localized. The cause of this high velocity dispersion is not evident from the observations and simulated analogs presented here.Comment: 27 pages, 15 figures, 6 table