Boundary Layers for the Navier-Stokes Equations¶of Compressible Fluids

Vanishing Shear Viscosity and Boundary Layer for the Navier–Stokes Equations with Cylindrical Symmetry

“…(1.5) In addition, Frid and Shelukhin [5] also proved the vanishing shear viscosity of global strong solutions for isentropic flows in the case of cylindric symmetry, and similar results can be found in [2,3,15] and references therein. This result was generalized to the non-isentropic flow in [8] with the heat conductivity coefficient satisfying C −1 (1 + θ q ) κ ≡ κ(ρ, θ) C(1 + θ q ), |κ ρ (ρ, θ )| C(1 + θ q ) (q > 1).…”

“…Frid and Shelukhin [5] first investigated the boundary layer effect of the compressible isentropic flow with cylindrical symmetry for the constant initial value, and proved the existence of the thickness of boundary layers (cf. Definition 1.2 below) as O(μ α )(0 < α < 1 2 ).…”

Boundary layers in parabolic perturbations of scalar conservation laws

“…The similar definition of δ(ε) was proposed by the authors in [7], with W 1,1 g (Ω) substituted by L ∞ (Ω), to justify the Stokes-Blasius law δ(µ) ∼ √ µ of the laminar boundary-layer thickness for axially symmetric flows of a compressible fluid between two cylinders when the shear viscosity µ is small and the dilatational viscosity is kept constant. In the present paper, the choice of W 1,1 g (Ω) is due to the fact that Ω is unbounded.…”

Regularity to the spherically symmetric compressible Navier–Stokes equations with density-dependent viscosity

“…We introduce the following coordinate transformation: 12) then the boundaries r = a and r = b become (1.14)…”