Geodesic
Stability threshold of two-dimensional Couette flow in Sobolev spaces
Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 2, pp. 245-325 Cet article a éte moissonné depuis la source Numdam

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We study the stability threshold of the two-dimensional Couette flow in Sobolev spaces at high Reynolds number Re. We prove that if the initial vorticity Ω in satisfies ∥Ω in -(-1)∥ H σ ≤ εRe -1/3 , then the solution of the two-dimensional Navier–Stokes equation approaches some shear flow which is also close to Couette flow for time t≫Re 1/3 by a mixing-enhanced dissipation effect, and then converges back to Couette flow when t→+∞.

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DOI : 10.4171/aihpc/8
Classification : 35B35, 35B40, 35Q30
Keywords: Couette flow, Sobolev Spaces 
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     author = {Masmoudi, Nader and Zhao, Weiren},
     title = {Stability threshold of two-dimensional {Couette} flow in {Sobolev} spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {245--325},
     year = {2022},
     volume = {39},
     number = {2},
     doi = {10.4171/aihpc/8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/8/}
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Masmoudi, Nader; Zhao, Weiren. Stability threshold of two-dimensional Couette flow in Sobolev spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 2, pp. 245-325. doi: 10.4171/aihpc/8

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