Low Mach number limit on thin domains

Low Mach Number Limit for Viscous Compressible Flows

In this survey paper, we are concerned with the zero Mach number limit for compressible viscous flows. For the sake of (mathematical) simplicity, we restrict ourselves to the case of barotropic fluids and we assume that the flow evolves in the whole space or satisfies periodic boundary conditions. We focus on the case of ill-prepared data. Hence highly oscillating acoustic waves are likely to p...

Multicomponent reactive flows : symmetrization and the low Mach number limit

We consider the equations governing multicomponent reactive flows derived from the kinetic theory of dilute polyatomic reactive gas mixtures. It was shown in [2] that there exists a generalized entropy which allows to derive a symmetric conservative form of the system. In the framework of Kawashima’s and Shizuta’s theory, we had recast the resulting system into a normal form, that is, in the fo...

Low Mach Number Limit of Viscous Compressible Magnetohydrodynamic Flows

The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant...

Low Mach number limit of the full Navier-Stokes equations,

The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniform...

Nečas Center for Mathematical Modeling Low Mach number limit for the Navier-Stokes system on unbounded domains under strong stratification