, Volume 216, Issue 3, pp 663-686

An Eulerian–Lagrangian Approach¶to the Navier–Stokes Equations

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We present a formulation of the incompressible viscous Navier–Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.

Received: 13 May 2000 / Accepted: 22 September 2000