Topical Problems of Fluid Mechanics


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

Time Delay and Lagrangian Differences for Viscous Incompressible Fluid Flow
Varnhorn W.
Abstract:
The motion of a viscous incompressible uid ow in bounded domains with a smooth bound- ary can be described by the nonlinear nonsteady Navier-Stokes equations. This description corresponds to the so-called Eulerian representation approach. We develop an approximation method for the Navier-Stokes system by a suitable coupling of the Eulerian and the Lagrangian representation of the ow, where the latter is de_ned 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 of the Navier-Stokes system in the sense of Leray-Hopf.
Keywords:
Navier-Stokes equations, time delay, Lagrangian differences

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In Proceedings Topical Problems of Fluid Mechanics 2015, Prague, 2015 Edited by David Šimurda and Tomáš Bodnár, pp. 255-260 ISBN 978-80-87012-55-0 (Print) ISSN 2336-5781 (Print)