GÉRARD-VARET , David

This paper is devoted to the equations of incompressible magnetohydrodynamics (MHD). Its general concern is the "dynamo effect", i.e. the growth of magnetic field through the movement of a conducting fluid. Motivated by the so-called "stretch-diffuse mechanism", we study the nonlinear stability of solutions (u, b = 0) where the velocity u is a...

We study the stability of two-dimensional solutions of the three-dimensional Navier-Stokes equations, in the limit of small viscosity. We are interested in steady flows with locally closed streamlines. We consider the so-called elliptic and centrifugal instabilities, which correspond to the continuous spectrum of the underlying linearized Euler...