Interface cinétique / fluide : Un modèle simplifié
Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity
In this short note we give a link between the regularity of the solution to the 3D Navier-Stokes equation and the behavior of the direction of the velocity . It is shown that the control of in a suitable norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based on very...
Regularity analysis for systems of reaction-diffusion equations
This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations. In particular, we show the global boundedness and regularity of the solutions in one and two dimensions. In addition, we discuss the Hausdorff dimension of the set of singularities in higher dimensions. Our approach is inspired by De Giorgi’s method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere...
Limites hydrodynamiques pour les équations de Vlasov-Stokes
On présente quelques problèmes et résultats de type limites hydrodynamiques pour des modèles couplés fluide/cinétique décrivant l'interaction de particules avec un fluide en mouvement.
-type contraction for systems of conservation laws
The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in . However it is not a contraction in for any . Leger showed in [] that for a convex flux, it is however a contraction in up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of systems. We treat in details two examples:...
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