An explicit potential theory for the stokes resolvent boundary value problems in three dimensions.
Finite differences and boundary element methods for non-stationary viscous incompressible flow
We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of...
Lagrangian approximations and weak solutions of the Navier-Stokes equations
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid....
On the boundness of the Stokes semigroup in two-dimensional exterior domains.
The Poisson equation in homogeneous Sobolev spaces.
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