Journal article
Navier‐Stokes Initial Value Problem for Boundary‐Free Incompressible Fluid Flow
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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Details
- Title
- Navier‐Stokes Initial Value Problem for Boundary‐Free Incompressible Fluid Flow
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- The Physics of fluids (1958), v 13(12), pp 2891-2903
- Publisher
- American Institute of Physics (AIP)
- Number of pages
- 13
- Resource Type
- Journal article
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1970I040100002
- Scopus ID
- 2-s2.0-3042986399
- Other Identifier
- 991019173748104721