Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids

We study strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in Omega subset of R-3. Deriving higher a priori estimates independent of the lower bounds of the density, we prove the existence and uniqueness of local strong solutions to the initial value problem (for Omega = R-3) or the initial boundary value problem (for Omega subset ofsubset of R-3) even though the initial density vanishes in an open subset of Omega, i.e., an initial vacuum exists. As an immediate consequence of the a priori estimates, we obtain a continuation theorem for the local strong solutions.