 
Summary: LOW MACH NUMBER FLOWS, AND COMBUSTION
THOMAS ALAZARD
Abstract. We prove uniform existence results for the full NavierStokes
equations for time intervals which are independent of the Mach num
ber, the Reynolds number and the P´eclet number. We consider general
equations of state and we give an application for the low Mach number
limit combustion problem introduced by Majda in [18].
1. Introduction
For a fluid with density , velocity v, pressure P, temperature T, internal
energy e, Lam´e coefficients , and coefficient of thermal conductivity k,
the full NavierStokes equations, written in a nondimensional way, are
(1.1)
t + div(v) = 0,
t(v) + div(v v) +
P
2
= µ 2 div(Dv) + ( div v) ,
