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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-33,
author = {Werner Varnhorn},
title = {Lagrangian approximations and weak solutions of the Navier-Stokes equations},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {515-532},
zbl = {1156.35446},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-33}
}
Werner Varnhorn. Lagrangian approximations and weak solutions of the Navier-Stokes equations. Banach Center Publications, Tome 83 (2008) pp. 515-532. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-33/