Lagrangian approximations and weak solutions of the Navier-Stokes equations

Werner Varnhorn. "Lagrangian approximations and weak solutions of the Navier-Stokes equations." Banach Center Publications 81.1 (2008): 515-532. <http://eudml.org/doc/281866>.

@article{WernerVarnhorn2008,
abstract = {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. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.},
author = {Werner Varnhorn},
journal = {Banach Center Publications},
keywords = {Navier-Stokes equation; Lagrangian approximation; weak solution},
language = {eng},
number = {1},
pages = {515-532},
title = {Lagrangian approximations and weak solutions of the Navier-Stokes equations},
url = {http://eudml.org/doc/281866},
volume = {81},
year = {2008},
}

TY - JOUR
AU - Werner Varnhorn
TI - Lagrangian approximations and weak solutions of the Navier-Stokes equations
JO - Banach Center Publications
PY - 2008
VL - 81
IS - 1
SP - 515
EP - 532
AB - 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. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.
LA - eng
KW - Navier-Stokes equation; Lagrangian approximation; weak solution
UR - http://eudml.org/doc/281866
ER -