1,166 research outputs found
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
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,
and , .
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 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
is a frequency localization on .Comment: 12page
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