Ancient Solutions to Navier–Stokes Equations in Half Space

In the present paper we consider mild bounded ancient (backward) solutions to the Navier–Stokes equations in the half plane. We give two different definitions, prove their equivalence and prove smoothness up to the boundary. Such solutions appear as a result of rescaling around a singular point of t...

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Bibliographic Details
Published in:Journal of mathematical fluid mechanics 2015-09, Vol.17 (3), p.551-575
Main Authors: Barker, T., Seregin, G.
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Physics
Physics and Astronomy
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Summary:In the present paper we consider mild bounded ancient (backward) solutions to the Navier–Stokes equations in the half plane. We give two different definitions, prove their equivalence and prove smoothness up to the boundary. Such solutions appear as a result of rescaling around a singular point of the initial boundary value problem for the Navier–Stokes equations in the half-plane.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-015-0211-z