Global solutions, structure of initial data and the Navier-Stokes equations

Piotr Bogusław Mucha

Banach Center Publications (2008)

  • Volume: 81, Issue: 1, page 277-286
  • ISSN: 0137-6934

Abstract

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In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.

How to cite

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Piotr Bogusław Mucha. "Global solutions, structure of initial data and the Navier-Stokes equations." Banach Center Publications 81.1 (2008): 277-286. <http://eudml.org/doc/282365>.

@article{PiotrBogusławMucha2008,
abstract = {In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.},
author = {Piotr Bogusław Mucha},
journal = {Banach Center Publications},
keywords = {global in time solutions; large data; stability; Navier-Stokes equations; structure of initial data; regularity},
language = {eng},
number = {1},
pages = {277-286},
title = {Global solutions, structure of initial data and the Navier-Stokes equations},
url = {http://eudml.org/doc/282365},
volume = {81},
year = {2008},
}

TY - JOUR
AU - Piotr Bogusław Mucha
TI - Global solutions, structure of initial data and the Navier-Stokes equations
JO - Banach Center Publications
PY - 2008
VL - 81
IS - 1
SP - 277
EP - 286
AB - In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.
LA - eng
KW - global in time solutions; large data; stability; Navier-Stokes equations; structure of initial data; regularity
UR - http://eudml.org/doc/282365
ER -

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