IJPAM: Volume 42, No. 2 (2008)

ON LAGRANGIAN APPROXIMATION
FOR THE NAVIER-STOKES SYSTEM

Werner Varnhorn
Fachbereich für Mathematik und Informatik
AG Analysis und Angewandte Mathematik
Universität Kassel
Heinrich-Plett Str. 40 (AVZ), Kassel, D-34132, GERMANY
e-mail: varnhorn@mathematik.uni-kassel.de


Abstract.The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes system (N). This description corresponds to the so-called Eulerian approach. We develop a new approximation method for (N) in the 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. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity, which contains a convergent subsequence with limit function $v$ such that $v$ is a weak solution on (N).

Received: August 17, 2007

AMS Subject Classification: 35B65, 35D05, 76D05

Key Words and Phrases: Navier-Stokes system, Lagrangian approximation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2