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Asymptotic Stability of Large Solutions with Large Perturbation to the Navier–Stokes Equations

✍ Scribed by Hideo Kozono

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
265 KB
Volume
176
Category
Article
ISSN
0022-1236

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✦ Synopsis

dedicated to professor hermann sohr on the occasion of his 60th birthday

Consider weak solutions w of the Navier Stokes equations in Serrin's class w # L : (0, ; L q (0)) for 2Â:+3Âq=1 with 3<q

, where 0 is a general unbounded domain in R 3 . We shall show that although the initial and external disturbances from w are large, every perturbed flow v with the energy inequality converges asymptotically to w as &v(t)&w(t)& L 2 (0) Ä 0, &{v(t)&{w(t)& L 2 (0) =O(t &1Â2 ) as t Ä .

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