We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the… (More)

Abstract. We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of… (More)

The purpose of this paper is to prove sharp global existence theorems in all dimensions for small-amplitude wave equations with power-type nonlinearities. For a given " power " p > 1, we shall… (More)

Abstract. We study the motion of a compressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the… (More)

We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = Cγ ρ γ for γ > 1. The vacuum… (More)

The set (m,R3+1, 0): standard Minkowski metric g = m = −dt2 + 3i=1(dxi)2 on R3+1 and vanishing scalar field ψ ≡ 0 describes the Minkowski space-time solution of the system (1.1). The problem of… (More)

Condition (1.3) says that the pressure p vanishes outside the domain and condition (1.4) says that the boundary moves with the velocity V of the fluid particles at the boundary. Given a domain D0 ⊂… (More)

has a global solution for all t ≥ 0 if initial data are sufficiently small. Here the curved wave operator is ̃g = g ∂α∂β, where we used the convention that repeated upper and lower indices are summed… (More)

We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the… (More)