558 research outputs found
Global Solutions for the Gravity Water Waves Equation in Dimension 3
We show existence of global solutions for the gravity water waves equation in
dimension 3, in the case of small data. The proof combines energy estimates,
which yield control of L^2 related norms, with dispersive estimates, which give
decay in L^\infty. To obtain these dispersive estimates, we use an analysis in
Fourier space; the study of space and time resonances is then the crucial
point
Uniform regularity for the Navier-Stokes equation with Navier boundary condition
We prove that there exists an interval of time which is uniform in the
vanishing viscosity limit and for which the Navier-Stokes equation with Navier
boundary condition has a strong solution. This solution is uniformly bounded in
a conormal Sobolev space and has only one normal derivative bounded in
. This allows to get the vanishing viscosity limit to the
incompressible Euler system from a strong compactness argument
A bio-inspired image coder with temporal scalability
We present a novel bio-inspired and dynamic coding scheme for static images.
Our coder aims at reproducing the main steps of the visual stimulus processing
in the mammalian retina taking into account its time behavior. The main novelty
of this work is to show how to exploit the time behavior of the retina cells to
ensure, in a simple way, scalability and bit allocation. To do so, our main
source of inspiration will be the biologically plausible retina model called
Virtual Retina. Following a similar structure, our model has two stages. The
first stage is an image transform which is performed by the outer layers in the
retina. Here it is modelled by filtering the image with a bank of difference of
Gaussians with time-delays. The second stage is a time-dependent
analog-to-digital conversion which is performed by the inner layers in the
retina. Thanks to its conception, our coder enables scalability and bit
allocation across time. Also, our decoded images do not show annoying artefacts
such as ringing and block effects. As a whole, this article shows how to
capture the main properties of a biological system, here the retina, in order
to design a new efficient coder.Comment: 12 pages; Advanced Concepts for Intelligent Vision Systems (ACIVS
2011
Regulation of durum wheat Na(+)/H (+) exchanger TdSOS1 by phosphorylation
We have identified a plasma membrane Na+/H+ exchanger from durum wheat, designated TdSOS1. Heterologous expression of TdSOS1 in a yeast strain lacking endogenous Na+ efflux proteins showed complementation of the Na+- and Li+-sensitive phenotype by a mechanism involving cation efflux. Salt tolerance conferred by TdSOS1 was maximal when co-expressed with the Arabidopsis protein kinase complex SOS2/SOS3. In vitro phosphorylation of TdSOS1 with a hyperactive form of the Arabidopsis SOS2 kinase (T/DSOS2∆308) showed the importance of two essential serine residues at the C-terminal hydrophilic tail (S1126, S1128). Mutation of these two serine residues to alanine decreased the phosphorylation of TdSOS1 by T/DSOS2∆308 and prevented the activation of TdSOS1. In addition, deletion of the C-terminal domain of TdSOS1 encompassing serine residues at position 1126 and 1128 generated a hyperactive form that had maximal sodium exclusion activity independent from the regulatory SOS2/SOS3 complex. These results are consistent with the presence of an auto-inhibitory domain at the C-terminus of TdSOS1 that mediates the activation of TdSOS1 by the protein kinase SOS2. Expression of TdSOS1 mRNA in young seedlings of the durum wheat variety Om Rabia3, using different abiotic stresses (ionic and oxidative stress) at different times of exposure, was monitored by RT–PCR.Peer Reviewe
Scattering for the Zakharov system in 3 dimensions
We prove global existence and scattering for small localized solutions of the
Cauchy problem for the Zakharov system in 3 space dimensions. The wave
component is shown to decay pointwise at the optimal rate of t^{-1}, whereas
the Schr\"odinger component decays almost at a rate of t^{-7/6}.Comment: Minor changes and referee's comments include
On the existence of solutions to the relativistic Euler equations in 2 spacetime dimensions with a vacuum boundary
We prove the existence of a wide class of solutions to the isentropic
relativistic Euler equations in 2 spacetime dimensions with an equation of
state of the form that have a fluid vacuum boundary. Near the fluid
vacuum boundary, the sound speed for these solutions are monotonically
decreasing, approaching zero where the density vanishes. Moreover, the fluid
acceleration is finite and bounded away from zero as the fluid vacuum boundary
is approached. The existence results of this article also generalize in a
straightforward manner to equations of state of the form
with .Comment: A major revision of the second half of the pape
Dynamical elastic bodies in Newtonian gravity
Well-posedness for the initial value problem for a self-gravitating elastic
body with free boundary in Newtonian gravity is proved. In the material frame,
the Euler-Lagrange equation becomes, assuming suitable constitutive properties
for the elastic material, a fully non-linear elliptic-hyperbolic system with
boundary conditions of Neumann type. For systems of this type, the initial data
must satisfy compatibility conditions in order to achieve regular solutions.
Given a relaxed reference configuration and a sufficiently small Newton's
constant, a neigborhood of initial data satisfying the compatibility conditions
is constructed
Multi-scale analysis of compressible viscous and rotating fluids
We study a singular limit for the compressible Navier-Stokes system when the
Mach and Rossby numbers are proportional to certain powers of a small parameter
\ep. If the Rossby number dominates the Mach number, the limit problem is
represented by the 2-D incompressible Navier-Stokes system describing the
horizontal motion of vertical averages of the velocity field. If they are of
the same order then the limit problem turns out to be a linear, 2-D equation
with a unique radially symmetric solution. The effect of the centrifugal force
is taken into account
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
Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition
In this paper, we investigate the vanishing viscosity limit for solutions to
the Navier-Stokes equations with a Navier slip boundary condition on general
compact and smooth domains in . We first obtain the higher order
regularity estimates for the solutions to Prandtl's equation boundary layers.
Furthermore, we prove that the strong solution to Navier-Stokes equations
converges to the Eulerian one in and
L^\infty((0,T)\times\o), where is independent of the viscosity, provided
that initial velocity is regular enough. Furthermore, rates of convergence are
obtained also.Comment: 45page
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