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

On A Stabilized Navier-Stokes System
W. Varnhorn
Abstract:
In the present paper we consider the non-stationary Navier-Stokes equations (N₀) in smoothly bounded domains G⊆ℝ³. We stabilize the nonlinear convective term with help of a time delay ε > 0 in its derivative-free part. Extending the given initial value in a suitable way to negative times the method leads to a well-posed initial boundary value problem (Nε), the unique solution of which has a high degree of regularity and satisfies the energy equation. Passing to the limit ε → 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N₀) in a weak sense (Hopf).
Keywords:
Navier-Stokes system, stabilization, strong solution, weak solution

Fulltext: PDF DOI: https://doi.org/10.14311/TPFM.2019.028

In Proceedings Topical Problems of Fluid Mechanics 2019, Prague, 2019 Edited by David Šimurda and Tomáš Bodnár, pp. 205-214 ISBN 978-80-87012-69-7 (Print) ISSN 2336-5781 (Print)