Diffusive Wave in the Low Mach Limit for Non-Viscous and Heat-Conductive Gas

TL;DR

This paper studies the low Mach number limit of a non-viscous, heat-conductive gas, demonstrating convergence to a nonlinear diffusion wave and revealing the relationship between wave velocity and temperature variation.

Contribution

It establishes the global convergence to a nonlinear diffusion wave for the low Mach limit in a non-viscous, heat-conductive gas system, extending understanding of wave behavior in such conditions.

Findings

Solution converges to a nonlinear diffusion wave as Mach number approaches zero.

Diffusion wave velocity is proportional to temperature variation.

Similar phenomena occur in the compressible Navier-Stokes system at small Mach numbers.

Abstract

The low Mach number limit for one-dimensional non-isentropic compressible Navier-Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the solution of the system converges to a nonlinear diffusion wave globally in time as Mach number goes to zero. It is remarked that the velocity of diffusion wave is proportional with the variation of temperature. Furthermore, it is shown that the solution of compressible Navier-Stokes system also has the same phenomenon when Mach number is suitably small.