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Licensed Unlicensed Requires Authentication Published by Oldenbourg Wissenschaftsverlag May 19, 2015

Time delay and Lagrangian approximation for Navier–Stokes flow

  • Nazgul Asanalieva EMAIL logo , Carolin Heutling and Werner Varnhorn
From the journal Analysis


We consider the nonstationary nonlinear Navier–Stokes equations describing the motion of a viscous incompressible fluid flow for 0<tT in a bounded domain Ω3 with sufficiently smooth boundary Ω. We use a particle method in connection with a time delay to approximate the nonlinear convective term by a single central Lagrangian difference quotient constructed from autonomous systems of ordinary differential equations. We show that the resulting approximate Navier–Stokes system has a uniquely determined global solution satisfying the energy equation and having a high degree of regularity uniformly in time. Moreover, we prove that the sequence of approximate solutions has an accumulation point satisfying the Navier–Stokes equations in a weak sense and the energy inequality.

Received: 2015-1-5
Revised: 2015-3-9
Accepted: 2015-4-30
Published Online: 2015-5-19
Published in Print: 2015-11-1

© 2015 by De Gruyter

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