Dynamics near the subcritical transition of the 3D Couette flow II above threshold case / Jacob Bedrossian, Pierre Germain, Nader Masmoudi.
| Author/creator | Bedrossian, Jacob, 1984- |
| Other author | Germain, Pierre, 1979- |
| Other author | Masmoudi, Nader, 1974- |
| Format | Electronic |
| Publication Info | Providence : American Mathematical Society, [2022] |
| Description | iii, 135 pages ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; volume 279, number 1377 |
| Contents | Outline of the proof -- Regularization and continuation -- Multiplier and paraproduct tools -- High norm estimate on Q2 -- High norm estimate on Q3 -- High norm estimate on Q10 -- High norm estimate on Q1/= -- Coordinate system controls -- Enhanced dissipation estimates -- Sobolev estimates. |
| Abstract | "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"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2022048386 |
| ISBN | 9781470472252 (paperback) |