For the 3D Navier–Stokes problem on the whole space, we study existence, regularity and stability of time-periodic solutions in Lebesgue, Lorentz or Sobolev spaces, when the periodic forcing belongs to critical classes of forces.

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, a neural network model reference adaptive system speed observer is designed, which can be used in speed control of linear induction motors (lims). dynamical equations of lim have been considered accurate. in other words, the end effect and the electrical losses of the motor have been included in the motor equivalent circuit. then equations of the reference model and adaptive mode...

in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.