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

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