The dependence of the fractal dimension global attractors for damped 3D Euler–Bardina equations on regularization parameter ? > 0 and Ekman damping coefficient ? is studied. We present explicit upper bounds this case whole space, periodic boundary conditions, bounded domain with Dirichlet conditions. sharpness these estimates when ? (which corresponds in limit to classical Euler equations) demo...

We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of the solutions to the second-grade fluid equations that does not vanish as t → ∞. Applications to the damped Euler equations are given.

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

An improved high order nite di erence method for low Mach number computational aeroacoustics (CAA) is described. The improvements involve the conditioning of the Euler equations to minimize numerical cancellation errors, and the use of a stable non-dissipative sixth-order central spatial interior scheme and a thirdorder boundary scheme. Spurious high frequency oscillations are damped by a third...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...

An improved high order nite di erence method for lowMach number computational aeroacoustics (CAA) is described. The improvements involve the conditioning of the Euler equations to minimize numerical cancellation errors, and the use of a stable non-dissipative sixth-order central spatial interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a third...

We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown that this system has a strong global and a strong trajectory attractor in the Sobolev space H. A similar result on the strong attraction holds in the spaces...