Dynamics near the subcritical transition of the 3D Couette flow I : below threshold case /

"We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. We prove that for sufficiently regular initial data of size [epsilon] [less than or equal to] c0Re-1 for some universal c0> 0, the solution is global,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bedrossian, Jacob, 1984- (Autor), Germain, Pierre, 1979- (Autor), Masmoudi, Nader, 1974- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2020]
Colección:Memoirs of the American Mathematical Society.
Temas:
Viscous flow > Mathematical models.
Stability.
Shear flow.
Inviscid flow.
Mixing.
Damping (Mechanics)
Three-dimensional modeling.
Écoulement visqueux > Modèles mathématiques.
Stabilité.
Écoulement cisaillé.
Écoulement non visqueux.
Mélange.
Amortissement (Mécanique)
Modélisation tridimensionnelle.
stability.
Estabilidad
Variedades en dimensión tres
Inviscid flow
Mixing
Shear flow
Stability
Three-dimensional modeling
Viscous flow > Mathematical models
Partial differential equations > Qualitative properties of solutions > Stability.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} > Hydrodynamic stability > Parallel shear flows.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} > Hydrodynamic stability > Nonlinear effects.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} > Turbulence [See also 37-XX, 60Gxx, 60Jxx] > Transition to turbulence.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} > Turbulence [See also 37-XX, 60Gxx, 60Jxx] > Shear flows.
Partial differential equations > Qualitative properties of solutions > Asymptotic behavior of solutions.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} > Turbulence [See also 37-XX, 60Gxx, 60Jxx] > Turbulent transport, mixing.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Outline of the proof
  • Regularization and continuation
  • High norm estimate on Q2
  • High norm estimate on Q3
  • High norm estimate on Q1/0
  • High norm estimate on Q1/[not equal]
  • Coordinate system controls
  • Enhanced dissipation estimates
  • Sobolev estimates.

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