La démonstration est basée sur un argument inductif faisant intervenir des estimations a
priori dans L2 et L∞. Les bornes L2 sont prouvées dans [5], texte complémentaire au …

We investigate the stabilizing effect of the vertical equilibrium magnetic field in the Rayleigh--
Taylor (RT) problem for a nonhomogeneous incompressible viscous magnetohydrodynamic …

We consider a viscous fluid of finite depth below the air, occupying a three-dimensional
domain bounded below by a fixed solid boundary and above by a free moving boundary …

We establish the stability/instability criteria for the stratified compressible magnetic Rayleigh–
Taylor (RT) problem in Lagrangian coordinates. More precisely, under the stability …

We consider the plasma-vacuum interface problem in a horizontally periodic slab impressed
by a uniform non-horizontal magnetic field. The lower plasma region is governed by the …

An $\mathrm {L} _1 $-maximal regularity theory for parabolic evolution equations inspired by
the pioneering work of Da Prato and Grisvard is developed. Besides of its own interest, the …

We consider the free boundary problem for two layers of immiscible, viscous, incompressible
fluid in a uniform gravitational field, lying above a general rigid bottom in a three …

We investigate the stabilizing effect of elasticity in the Rayleigh–Taylor (RT) problem of
stratified immiscible viscoelastic fluids, separated by a free interface and in the presence of a …

Based on a bootstrap instability method, we prove the existence of unstable strong solutions
in the sense of L 1-norm to an abstract Rayleigh–Taylor (RT) problem arising from stratified …

We consider the dynamics of two layers of incompressible electrically conducting fluid
interacting with a magnetic field, which are confined within a 3D horizontally infinite slab and …