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. 249-255ISBN 978-80-87012-74-1 (Print)ISSN 2336-5781 (Print) |