The initial boundary value problem for inviscid barotropic fluid motion

Initial-Boundary Value Problem for Hyperbolic Equations

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

Initial-boundary value problem for the spherically symmetric Einstein equations for a perfect fluid

I1 is shown thal for a given spherically symmelric disvibution of a perfect Huid on a spacelike hypersurface wiul boundary and a piven. time-dependent boundary prt?sure. there exis15 a unique, local-in-lime solution of the Einstein equations. A Schwmchild spacetime can be allached to h e Huid bady i f and only if the boundary prcssurc vanishes. We asume a smooth equation of slate for which UW d...

On the Initial-boundary Value Problem for a Bingham Fluid in a Three Dimensional Domain

The initial-boundary value problem associated with the motion of a Bingham fluid is considered. The existence and uniqueness of strong solution is proved under a certain assumption on the data. It is also shown that the solution exists globally in time when the data are small and that the solution converges to a periodic solution if the external force is time-periodic 0. Introduction. The purpo...

The Initial Boundary Value Problem for Einstein’s Vacuum Field Equation

We study the initial boundary value problem for Einstein’s vacuum field equation. We prescribe initial data on an orientable, compact, 3-dimensional manifold S with boundary 6 6= ∅ and boundary conditions on the manifold T = R0 × 6. We assume the boundaries 6 and {0} × 6 of S and T to be identified in the natural way. Furthermore, we prescribe certain gauge source functions which determine the ...

An initial - boundary - value problem for the Korteweg -