Nombres de Reynolds, stabilité et Navier-Stokes
A generalization of a theorem by Kato on Navier-Stokes equations.
We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,∞);L(R)). More precisely, we show that if the initial data are sufficiently oscillating, in a suitable Besov space, then Kato's solution exists globally. As a corollary to this result, we obtain a theory of existence of self-similar solutions for the Navier-Stokes equations.
On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations.
We derive various estimates for strong solutions to the Navier-Stokes equations in C([0,T),L(R)) that allow us to prove some regularity results on the kinematic bilinear term.
Fonctions de Lyapunov pour les équations de Navier-Stokes
Asymptotic stability of Navier-Stokes flow past an obstacle
Results on the asymptotic stability of solutions of the exterior Navier-Stokes problem in ℝ³ are proved in the framework of weak spaces.
The Cauchy problem for the magneto-hydrodynamic system
We study the uniqueness and regularity of Leray-Hopf's weak solutions for the MHD equations with dissipation and resistance in different frameworks. Using different kinds of space-time estimates in conjunction with the Littlewood-Paley-Bony decomposition, we present some general criteria of uniqueness and regularity of weak solutions to the MHD system, and prove the uniqueness and regularity criterion in the framework of mixed space-time Besov spaces by applying Tao's trichotomy method.
Page 1