In this paper, we study the quasineutral limit of the isothermal Euler-Poisson equation for ions, in a domain with boundary. This is a follow-up to our previous work [5], devoted to no-penetration as well as subsonic outflow boundary conditions. We focus here on the case of supersonic outflow velocities. The structure of the boundary layers and the stabilization mechanism are different.
We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary L² decay for weak solutions is also established.
We study the Cauchy problem for the MHD system, and provide two regularity conditions involving horizontal components (or their gradients) in Besov spaces. This improves previous results.
Nous démontrons dans cet article que le système MHD tridimensionnel à densité et viscosité variables est localement bien posé lorsque pour et la densité initiale est proche d’une constante strictement positive. Nous démontrons également un résultat d’existence et d’unicité dans l’espace de Sobolev pour sans aucune condition de petitesse sur la densité.
This paper deals with a system of equations describing the motion of viscous electrically conducting incompressible fluid in a bounded three dimensional domain whose boundary is perfectly conducting. The displacement current appearing in Maxwell’s equations, is not neglected. It is proved that for a small periodic force and small positive there exists a locally unique periodic solution of the investigated system. For , these solutions are shown to convergeto a solution of the simplified (and...