DELAYED SINGULARITY FORMATION IN 2D COMPRESSIBLE FLOW

The initial value problem for the compressible Euler equations in two space dimensions is studied. Of interest is the lifespan of classical solutions with initial data that is a small perturbation from a consta nt state. The approach taken is to regard the compressible solution as a nonlinear superposition of an underlying incompressible flow and an irrotational compressible how This viewpoint yields an improvement fo r the lifespan over that given by standard existence theory. The estim ate for the lifespan is further improved when the initial data possess es certain symmetry. In the case of rotational symmetry, a result of S . Alinhac is reconsidered. The approach is also applied to the study o f the incompressible limit. The analysis combines energy and decay est imates based on vector fields related to the natural invariance of the equations.