Estimates for the three α-models known as the LANS-α, Leray-α and Bardina models are found in terms a Reynolds number associated with a Navier-Stokes velocity field. They are tabulated for comparative purposes and show clearly that all estimates for the Leray-α model are smaller than those for the LANS-α and Bardina models.

We consider the open problem of regularity for L3,∞-solutions to the Navier-Stokes equations. We show that the problem can be reduced to a backward uniqueness problem for the heat operator with lower order terms. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.

In this paper we prove the nonexistence of global weak solutions to the compressible Navier-Stokes equations for the isentropic gas in R N , N ≥ 3, where the pressure law given by p(ρ) = aρ γ , a > 0, 1 < γ ≤

We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in H, r ≥ 1/2 and prove a stability result for the analyticity radius.

This paper concerns the two-dimensional NavierStokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞(∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c1G + c2Re, where G is the Grashof number and Re the Reynolds number.

A micromixer with unbalanced three-split rhombic sub-channels was proposed, and analyses of the mixing and flow characteristics of this micromixer were performed in this work. Three-dimensional Navier-Stokes equations in combination with an advection-diffusion model with two working fluids (water and ethanol) were solved for the analysis. The mixing index and pressure drop were evaluated and co...

In this paper, we perform an input-output analysis of the linearized Navier-Stokes equations by investigating their spatio-temporal ’impulse response’. Our first motivation for this problem comes from experimental work, where transition to turbulence is observed to occur either naturally, with so-called ’turbulent spots’, or when these spots are intentionally induced in the flow by deliberate e...

The tradition in Navier-Stokes analysis of finding estimates in terms of the Grashof number Gr , whose character depends on the ratio of the forcing to the viscosity ν, means that it is difficult to make comparisons with other results expressed in terms of Reynolds number Re, whose character depends on the fluid response to the forcing. The first task of this paper is to apply the approach of D...

A small parameter technique is used to derive Reynolds' lubrication equation from the Stokes equation. The error associated with the approximation is estimated in suitable norms.

We show that L3,∞-solutions to the three-dimensional NavierStokes equations near a flat part of the boundary are smooth. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.