Topical Problems of Fluid Mechanics


logo UT logo CTU logo MIO Universite logo ERCOFTAC
Institute of Thermomechanics AS CR, v.v.i. CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics MIO Université du Sud Toulon Var - AMU - CNRS - IRD Czech Pilot centre ERCOFTAC
A Lagrangian Approach for Weak Solutions of the Navier-Stokes Equations

Varnhorn W.

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 both the stationary and the nonstationary 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).

Keywords:
Navier-Stokes Equations, Weak Solutions, Lagrangian Approach
Fulltext: PDF
DOI: https://doi.org/10.14311/TPFM.2020.032
In Proceedings Topical Problems of Fluid Mechanics 2020, Prague, 2020 Edited by David Šimurda and Tomáš Bodnár, pp. 249-255
ISBN 978-80-87012-74-1 (Print)
ISSN 2336-5781 (Print)
imce   Powered by Imce 3.0  © 2014, Pavel Formánek, Institute of Thermomechanics AS CR, v.v.i. [generated: 0.1518s]