The low Mach number limit for the isentropic Euler system with axisymmetric initial data

Low-mach-number Euler Equations with Solid-wall Boundary Condition and General Initial Data

Abstract. We prove that the divergence-free component of the compressible Euler equations with solid-wall boundary condition converges strongly towards the incompressible Euler equations at the same order as the Mach number. General initial data are considered and are not necessarily close to the divergence-free state. Thus, large amplitude of fast oscillations persist and interact through nonl...

Fujita Kato solution for compressible Navier-Stokes equation with axisymmetric initial data and zero Mach number limit

In this paper we investigate the question of the existence of global strong solution for the compressible Navier Stokes equations for small initial data such that the rotational part of the velocity Pu0 belongs to Ḣ N 2 −1. We show then an equivalence of the so called Fujita Kato theorem to the case of the compressible Navier-Stokes equation when we consider axisymmetric initial data in dimensi...

Study of a New Asymptotic Preserving Scheme for the Euler System in the Low Mach Number Limit

This article deals with the discretization of the compressible Euler system for all Mach numbers regimes. For highly subsonic flows, since acoustic waves are very fast compared to the velocity of the fluid, the gas can be considered as incompressible. From the numerical point of view, when the Mach number tends to zero, the classical Godunov type schemes present two main drawbacks: they lose co...

Viscosity Limit for Multidimensional Euler Equations for Compressible, Isentropic Fluid Flows with Radial Symmetry and Large Initial Data

Stability of Isentropic Navier–Stokes Shocks in the High-Mach Number Limit∗

By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier–Stokes equations with γ -law pressure (i) in the limit as Mach number M goes to infinity, for any γ ≥ 1 (proved analytically), and (ii) for M ≥ 2, 500, γ ∈ [1, 2.5] or M ≥ 13, 000, γ ∈ [2.5, 3] (demonstrated numerically)....