Abstract:In this paper, we establish the unique existence and some decay properties of a global solution of a free boundary problem of the incompressible Navier-Stokes equations in Lp in time and Lq in space framework in a uniformly H 2 ∞ domain Ω ⊂ R N for N ≥ 4. We assume the unique solvability of the weak Dirichlet problem for the Poisson equation and the Lq-Lr estimates for the Stokes semigroup. The novelty of this paper is that we do not assume the compactness of the boundary, which is essentially used in the case… Show more
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