Decaying solution of a Navier-Stokes flow without surface tension

Numerical Solution of Steady Free-Surface Navier-Stokes Flow

The usual time integration approach for solving steady viscous free surface flow problems has several drawbacks. We propose instead an efficient iterative method, which relies on a different but equivalent formulation of the free surface flow problem, involving a so-called quasi free-surface condition. Furthermore, we present a method for analyzing the properties of wave solutions of the discre...

Efficient Numerical Solution of SteadyFree-Surface Navier–Stokes Flow

Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic condition, and the Navier– Stokes equations subject to the dynamic conditions, until steady state is re...

On the two-phase Navier–Stokes equations with surface tension

In this paper we consider a free boundary problem that describes the motion of two viscous incompressible capillary Newtonian fluids. The fluids are separated by an interface that is unknown and has to be determined as part of the problem. Let Ω1(0) ⊂ Rn+1 (n > 1) be a region occupied by a viscous incompressible fluid, fluid1, and letΩ2(0) be the complement of the closure ofΩ1(0) in Rn+1, corre...

Existence of Navier-stokes Flow in the Half Space with Non-decaying Initial Data

Slowly Decaying Solutions to Incompressible Navier-stokes System

We study the large time asymptotics of solutions to the Cauchy problem in R for the incompressible Navier-Stokes system. Imposed assumptions on initial data imply that, at the first approximation, solutions look as solutions to the linear heat equation. The main goal of this work is to derive second terms of the asymptotic expansions of solutions and to extend, in this way, the results by Fujig...