Abstract
AbstractWe consider the initial boundary value problem for the nonstationary Navier‐Stokes equations in a bounded three dimensional domain Ω with a sufficiently smooth compact boundary ∂Ω. These equations describe the motion of a viscous incompressible fluid contained in Ω for 0 < t < T and represent a system of nonlinear partial differential equations concerning four unknown functions: the velocity vector v = (v1 (t, x), v2 (t, x), v3 (t, x)) and the kinematic pressure function p = p(t, x) of the fluid at time t ∈ (0, T) in x ∈ Ω. The purpose of this paper is to construct a regularized Navier‐Stokes system, which can be solved globally in time. Our construction is based on a coupling of the Lagrangian and the Eulerian representation of the fluid flow. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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