We study strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R3. 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 Ω = R3) or the initial boundary value problem (for Ω ⊂ ⊂ R3) even though the initial density vanishes in an open subset of Ω, 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics