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Transition threshold for the 3D Couette flow in a finite channel / Qi Chen, Dongyi Wei, Zhifei Zhang

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 296, number 1478 (April 2024)Publisher: Providence : American Mathematical Society, April 2024Description: v, 178 SeitenISBN:
  • 9781470468958
Subject(s): Additional physical formats: No title | 9781470478155 | Erscheint auch als: Transition Threshold for the 3D Couette Flow in a Finite Channel. Online-Ausgabe 1st ed. Providence : American Mathematical Society, 2024. 1 online resource (190 pages) | Erscheint auch als: Transition threshold for the 3D Couette flow in a finite channel. Online-Ausgabe Providence : American Mathematical Society, 2024. 1 Online-Ressource (v, 178 Seiten)DDC classification:
  • 530.15/1864 23/eng20240823
MSC: MSC: 35Q30LOC classification:
  • QA929
Summary: "In this paper, we study nonlinear stability of the 3D plane Couette flow (y, 0, 0) at high Reynolds number Re in a finite channel T 1, 1 T. It is well known that the plane Couette flow is linearly stable for any Reynolds number. However, it could become nonlinearly unstable and transition to turbulence for small but finite perturbations at high Reynolds number. This is so-called Sommerfeld paradox. One resolution of this paradox is to study the transition threshold problem, which is concerned with how much disturbance will lead to the instability of the flow and the dependence of disturbance on the Reynolds number. This work shows that if the initial velocity v0 satisfies v0 (y, 0, 0) H2 c0Re 1 for some c0 0 independent of Re, then the solution of the 3D Navier-Stokes equations is global in time and does not transit away from the Couette flow in the L sense, and rapidly converges to a streak solution for t Re 1 3 due to the mixing-enhanced dissipation effect. This result confirms the threshold result obtained by Chapman via an asymptotic analysis(JFM 2002). The most key ingredient of the proof is the resolvent estimates for the full linearized 3D Navier-Stokes system around the flow (V (y, z), 0, 0), where V (y, z) is a small perturbation(but independent of Re) of y"--PPN: PPN: 189675001X
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-296.2024,1478 Nicht ausleihbar
Total holds: 0
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