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Level Sets of the Vorticity and the Stream Function for the 2D Periodic Navier–Stokes Equations with Potential Forces

✍ Scribed by Igor Kukavica

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
578 KB
Volume
126
Category
Article
ISSN
0022-0396

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✦ Synopsis

By a result of Foias and Saut, the quotient of the enstrophy and the energy of a solution of the Navier Stokes equations with potential forces converges to the square root of an eigenvalue 4 k of the Stokes operator. We study the Hausdorff length (H 1 ) of the level sets of the vorticity and the stream function of solutions. We provide upper bounds for these quantities, and for large t we express them in terms of the corresponding eigenvalue 4 k .

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