A well-posedness theorem for non-homogeneous inviscid fluids via a perturbation theorem (Q1824094)

The author considers the nonlinear hyperbolic system of Euler equations for incompressible, inviscid, non-homogeneous flows. He proves the continuous dependence of solutions, that lie in appropriate Sobolev spaces, on the initial data and external forces. The proof uses Kato's perturbation theory for nonlinear hyperbolic evolution equations. The case of bounded domains is included in the results.