LIFETIME OF REGULAR SOLUTIONS OF 2-DIMENSIONAL AXIALLY SYMMETRICAL COMPRESSIBLE EULER EQUATIONS

We consider the 2D isentropic Euler equations; for rotationnally invariant data which are a perturbation of size epsilon of a rest state, we establish the first term asymptotic of the life span T(epsilon) of the classical solution (lim epsilon2 T(epsilon) = tau*2). Moreover, we give, for t less-than-or-equal-to A2/epsilon2 (A < tau*) an estimate of the true solution, by computing the size of its difference with an approximate solution obtained in a previous work.