Existence, Uniqueness and Regularity for the Second-Gradient Navier-Stokes Equations in Exterior Domains

Risultato della ricerca: Contributo in libroChapter

Abstract

We study the well-posedness of the problem ⎧ ⎪ ⎨ ⎪ ⎩ ∂u ∂t + (Du)u + ∇p = νΔu − τΔΔu in ]0,+∞[×Ω, divu = 0 in ]0,+∞[×Ω, u(t,x) = ∂u ∂n (t,x) = 0 on ]0,+∞[×∂Ω, u(0,x) = u 0 (x) in Ω, where u :]0,+∞[×Ω → R n is the velocity field, p :]0,+∞[×Ω → R is the pressure, ν is the kinematical viscosity, τ the so-called hyperviscosity and Ω is a general domain as for existence and uniqueness of the solution, and an exterior domain as for regularity results. This problem has been physically well motivated in the recent years as the simplest case of an isotropic second-order fluid, i.e. a fluid whose power expended depends on second derivatives of the velocity field.
Lingua originaleEnglish
Titolo della pubblicazione ospiteWaves in Flows
EditorTomaš Bodnar, Giovanni P. Galdi, Šarka Nečasová
Pagine181-202
Numero di pagine22
DOI
Stato di pubblicazionePubblicato - 2021

Keywords

  • Fluid Mechanics
  • Navier-Stokes equations

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