645 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
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
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 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
Observation comparative du dĂ©placement ionique dans les couches minces de PbF2 ÎČ et de CaF2 par diffusion Rutherford
Des couches minces de PbF2 ÎČ et de CaF2, dont les conductivitĂ©s ioniques sont trĂšs diffĂ©rentes, ont Ă©tĂ© analysĂ©es par rĂ©tro-diffusion de particules α. On a pu observer, dans le cas de PbF2, une variation importante du rapport des concentrations fluor/plomb dans l'Ă©paisseur de la couche, correspondant Ă une accumulation de fluor du cĂŽtĂ© du faisceau incident. Cet effet est attĂ©nuĂ© dans les couches de CaF2. L'interprĂ©tation des rĂ©sultats est basĂ©e sur l'existence d'un nombre important de dĂ©fauts crĂ©Ă©s par le faisceau, et sur leur dĂ©placement sous l'effet de la charge superficielle due Ă l'Ă©mission secondaire d'Ă©lectrons
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
Global exponential stability of classical solutions to the hydrodynamic model for semiconductors
In this paper, the global well-posedness and stability of classical solutions
to the multidimensional hydrodynamic model for semiconductors on the framework
of Besov space are considered. We weaken the regularity requirement of the
initial data, and improve some known results in Sobolev space. The local
existence of classical solutions to the Cauchy problem is obtained by the
regularized means and compactness argument. Using the high- and low- frequency
decomposition method, we prove the global exponential stability of classical
solutions (close to equilibrium). Furthermore, it is also shown that the
vorticity decays to zero exponentially in the 2D and 3D space. The main
analytic tools are the Littlewood-Paley decomposition and Bony's para-product
formula.Comment: 18 page
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 . 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 is in . 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
Formation of singularities in solutions to ideal hydrodynamics of freely cooling inelastic gases
We consider solutions to the hyperbolic system of equations of ideal granular
hydrodynamics with conserved mass, total energy and finite momentum of inertia
and prove that these solutions generically lose the initial smoothness within a
finite time in any space dimension for the adiabatic index Further, in the one-dimensional case we introduce a solution
depending only on the spatial coordinate outside of a ball containing the
origin and prove that this solution under rather general assumptions on initial
data cannot be global in time too. Then we construct an exact axially symmetric
solution with separable time and space variables having a strong singularity in
the density component beginning from the initial moment of time, whereas other
components of solution are initially continuous.Comment: 13 pages, 3 figure
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