579 research outputs found

    Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations

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    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 B∞,∞−1B^{-1}_{\infty,\infty} 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

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    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

    NGC 4254: An Act of Harassment Uncovered by the Arecibo Legacy Fast ALFA Survey

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    We present an HI map constructed from the Arecibo Legacy Fast ALFA (ALFALFA) survey of the surroundings of the strongly asymmetric Virgo cluster Sc galaxy NGC 4254. Noted previously for its lopsided appearance, rich interstellar medium, and extradisk HI emission, NGC 4254 is believed to be entering the Virgo environment for the first time and at high speed. The ALFALFA map clearly shows a long HI tail extending ~250 kpc northward from the galaxy. Embedded as one condensation within this HI structure is the object previously identified as a "dark galaxy": Virgo HI21 (Davies et al. 2004). A body of evidence including its location within and velocity with respect to the cluster and the appearance and kinematics of its strong spiral pattern, extra-disk HI and lengthy HI tail is consistent with a picture of "galaxy harassment" as proposed by Moore et al. (1996a,b; 1998). The smoothly varying radial velocity field along the tail as it emerges from NGC 4254 can be used as a timing tool, if interpreted as resulting from the coupling of the rotation of the disk and the collective gravitational forces associated with the harassment mechanism.Comment: accepted for publication in Ap.J.(Lett.). higher resolution figure available at http://egg.astro.cornell.edu/alfalfa/pubs/figs/n4254_f1.ep

    Observation comparative du dĂ©placement ionique dans les couches minces de PbF2 ÎČ et de CaF2 par diffusion Rutherford

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    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

    On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces

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    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

    Global exponential stability of classical solutions to the hydrodynamic model for semiconductors

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    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

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    This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N≄2N\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 ρ0\rho_{0} is in H1H^{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

    Development of singularities for the compressible Euler equations with external force in several dimensions

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    We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page
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