Stability of Constant Solutions to the Navier-Stokes System in ℝ³

Piotr Bogusław Mucha

Applicationes Mathematicae (2001)

  • Volume: 28, Issue: 3, page 301-310
  • ISSN: 1233-7234

Abstract

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The paper examines the initial value problem for the Navier-Stokes system of viscous incompressible fluids in the three-dimensional space. We prove stability of regular solutions which tend to constant flows sufficiently fast. We show that a perturbation of a regular solution is bounded in W r 2 , 1 ( ℝ ³ × [ k , k + 1 ] ) for k ∈ ℕ. The result is obtained under the assumption of smallness of the L₂-norm of the perturbing initial data. We do not assume smallness of the W r 2 - 2 / r ( ℝ ³ ) -norm of the perturbing initial data or smallness of the L r -norm of the perturbing force.

How to cite

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Piotr Bogusław Mucha. "Stability of Constant Solutions to the Navier-Stokes System in ℝ³." Applicationes Mathematicae 28.3 (2001): 301-310. <http://eudml.org/doc/279036>.

@article{PiotrBogusławMucha2001,
abstract = {The paper examines the initial value problem for the Navier-Stokes system of viscous incompressible fluids in the three-dimensional space. We prove stability of regular solutions which tend to constant flows sufficiently fast. We show that a perturbation of a regular solution is bounded in $W^\{2,1\}_r(ℝ³×[k,k+1])$ for k ∈ ℕ. The result is obtained under the assumption of smallness of the L₂-norm of the perturbing initial data. We do not assume smallness of the $W^\{2-2/r\}_r(ℝ³)$-norm of the perturbing initial data or smallness of the $L_r$-norm of the perturbing force.},
author = {Piotr Bogusław Mucha},
journal = {Applicationes Mathematicae},
keywords = {Navier-Stokes equations; global solution; large data; stability of regular solutions; smallness assumption},
language = {eng},
number = {3},
pages = {301-310},
title = {Stability of Constant Solutions to the Navier-Stokes System in ℝ³},
url = {http://eudml.org/doc/279036},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Piotr Bogusław Mucha
TI - Stability of Constant Solutions to the Navier-Stokes System in ℝ³
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 3
SP - 301
EP - 310
AB - The paper examines the initial value problem for the Navier-Stokes system of viscous incompressible fluids in the three-dimensional space. We prove stability of regular solutions which tend to constant flows sufficiently fast. We show that a perturbation of a regular solution is bounded in $W^{2,1}_r(ℝ³×[k,k+1])$ for k ∈ ℕ. The result is obtained under the assumption of smallness of the L₂-norm of the perturbing initial data. We do not assume smallness of the $W^{2-2/r}_r(ℝ³)$-norm of the perturbing initial data or smallness of the $L_r$-norm of the perturbing force.
LA - eng
KW - Navier-Stokes equations; global solution; large data; stability of regular solutions; smallness assumption
UR - http://eudml.org/doc/279036
ER -

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