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Navier‐Stokes Initial Value Problem for Boundary‐Free Incompressible Fluid Flow
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Navier‐Stokes Initial Value Problem for Boundary‐Free Incompressible Fluid Flow

Gerald Rosen
The Physics of fluids (1958), v 13(12), pp 2891-2903
Dec 1970

Abstract

Convergence proofs are reported for a general local iteration solution to the Navier‐Stokes initial value problem and estimates of the accuracy of the n th iterative approximation are derived. Without appeal to methods of functional analysis, it is shown that a Kiselev‐Ladyzhenskaya weak solution is, in fact, a classical solution. Any one of three alternative conditions on the initial velocity field is found to be sufficient to guarantee the existence of a global solution. Breakdown phenomenon which may prevent a local solution from being continued for all t ≥ 0 to a global solution is analyzed. The mathematical theory suggests that breakdown is precluded for a suitably smooth initial velocity field, irrespective of the over‐all initial velocity field magnitude.

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