Media type: E-Article Title: The Navier‐Stokes equations with particle methods Contributor: Asanalieva, Nazgul; Heutling, Carolin; Varnhorn, Werner imprint: Wiley, 2014 Published in: PAMM Language: English DOI: 10.1002/pamm.201410352 ISSN: 1617-7061 Keywords: General Medicine Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>We consider the initial boundary value problem for the nonstationary Navier‐Stokes equations in a bounded three‐dimensional domain Ω with a sufficiently smooth boundary ∂Ω. These equations describe the motion of a viscous incompressible fluid contained in Ω for 0 < <jats:italic>t</jats:italic> < <jats:italic>T</jats:italic>. They represent a system of nonlinear partial differential equations concerning four unknown functions, i.e. the velocity vector <jats:italic>v</jats:italic> = (<jats:italic>v</jats:italic><jats:sub>1</jats:sub>(<jats:italic>t, x</jats:italic>), <jats:italic>v</jats:italic><jats:sub>2</jats:sub>(<jats:italic>t, x</jats:italic>), <jats:italic>v</jats:italic><jats:sub>3</jats:sub>(<jats:italic>t, x</jats:italic>)) and the kinematic pressure function <jats:italic>p</jats:italic> = <jats:italic>p</jats:italic>(<jats:italic>t, x</jats:italic>) of the fluid at time <jats:italic>t</jats:italic> ∈ (0, <jats:italic>T</jats:italic>) in <jats:italic>x</jats:italic> ∈ Ω. The purpose of this paper is to construct a Leray‐Hopf type weak solution to the nonstationary Navier‐Stokes system, which exists globally in time. Our construction is based on a suitable approximation using particle methods for stationary fluid flow. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)</jats:p> Access State: Open Access