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Dynamics near the subcritical transition of the 3D Couette flow II : above threshold case
This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re. In this work, we show that there is constant , independent of Re, such that sufficiently regular disturbances of size...
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| Auteurs principaux : | , , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Dynamics near the subcritical transition of the 3D Couette flow II : above threshold case / Jacob Bedrossian, Pierre Germain, Nader Masmoudi |
| Publié : |
Providence (R.I.) :
American Mathematical Society
, 2022 |
| Description matérielle : | 1 vol. (V-135 pages) |
| Collection : | Memoirs of the American Mathematical Society ; 1377 |
| Sujets : | |
| Documents associés : | Autre format:
Dynamics near the subcritical transition of the 3D Couette flow II:above threshold case |
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| 200 | 1 | |a Dynamics near the subcritical transition of the 3D Couette flow II |e above threshold case |f Jacob Bedrossian, Pierre Germain, Nader Masmoudi | |
| 214 | 0 | |a Providence (R.I.) |c American Mathematical Society |d 2022 | |
| 215 | |a 1 vol. (V-135 pages) |d 26 cm | ||
| 225 | 2 | |a Memoirs of the American Mathematical Society |x 0065-9266 |v number 1377 | |
| 320 | |a Bibliogr. p. 133-135 | ||
| 330 | |a This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re. In this work, we show that there is constant , independent of Re, such that sufficiently regular disturbances of size for any exist at least until and in general evolve to be due to the lift-up effect. Further, after times , the streamwise dependence of the solution is rapidly diminished by a mixing-enhanced dissipation effect and the solution is attracted back to the class of "2.5 dimensional" streamwise-independent solutions (sometimes referred to as "streaks"). The largest of these streaks are expected to eventually undergo a secondary instability at . Hence, our work strongly suggests, for all (sufficiently regular) initial data, the genericity of the "lift-up effect streak growth streak breakdown" scenario for turbulent transition of the 3D Couette flow near the threshold of stability forwarded in the applied mathematics and physics literature |2 résumé des auteurs | ||
| 359 | 2 | |b Outline of the proof |b Regularization and continuation |b Multiplier and paraproduct tools |b High norm estimate on Q |b High norm estimate on Q |b High norm estimate on Q |b High norm estimate on Q /= |b Coordinate system controls |b Enhanced dissipation estimates |b Sobolev estimates | |
| 410 | | | |0 013293931 |t Memoirs of the American Mathematical Society |x 0065-9266 |v 1377 | |
| 452 | | | |t Dynamics near the subcritical transition of the 3D Couette flow II:above threshold case |y 978-1-4704-7231-3 | |
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