We address the study of decay rates of solutions to dissipative equations. The
characterization of these rates is given for a wide class of linear systems by the decay …

We address the question of convergence to the incompressible Navier-Stokes equations for
slightly compressible viscous flows with ill-prepared initial data and periodic boundary …

We are concerned with the existence and uniqueness of local or global solutions for slightly
compressible viscous fluids in the whole space. In [6] and [7], we proved local and global …

Magnetohydrodynamics (MHD) is the study of the interaction of electrically conducting fluids
in the presence of magnetic fields. MHD applications require substantially more efficient …

In this article, we present, analyze, and test a first-order implicit-explicit type scheme based
on the artificial compressibility (AC) method and the scalar auxiliary variable (SAV) …

Ces notes sont issues de deux cours de DEA. Dès 1996, à l'initiative de l'un d'entre nous (Y.
Maday), fut en effet créé au sein du DEA d'Analyse numérique de Paris VI un cours de …

The time-dependent Schrödinger equation for a Coulomb collision between a heavy point
charge and a harmonically bound electron is solved exactly numerically. The energy …

On s' intéresse à des problèmes mixtes pour des systèmes symétriques hyperboliques
multidimensionnels quasilinéaires avec des conditions aux limites maximales dissipatives …

In this article, we use the decay character of initial data to compare the energy decay rates of
solutions to different compressible approximations to the Navier-Stokes equations. We show …

Computational fluid dynamics is an essential research area that is of crucial importance in
comprehending of fluid flows in mechanical and hydrodynamic processes. Accurate, efficient …