In this paper it is attempted to investigate the behavior of an inviscid flow in the meridional plane of an axial flow compressor. For this purpose the 3-D unsteady Euler equations in cylindrical coordinate are averaged in tangential direction. Therefore, the equations are reduced to a 2-D system. By averaging the tangential component of momentum equation, a blade force will result. Axial and r...

Nonlocally related systems for the Euler and Lagrange systems of twodimensional dynamical nonlinear elasticity are constructed. Using the continuity equation, i.e., conservation of mass of the Euler system to represent the density and Eulerian velocity components as the curl of a potential vector, one obtains the Euler potential system that is nonlocally related to the Euler system. It is shown...

In this paper, we define and study Hyers–Ulam stability of order 1 for Euler’s equation m−1 the Euler–Poisson in calculus variations two special cases, when these equations have form y″(x)=f(x) y(m)(x)=f(x), respectively. We prove some estimations Jyx−Jy0x, where y is an approximate solution y0 exact corresponding Euler Euler-Poisson equations, also give examples.

An Euler equation is a difference or differential equation that is an intertemporal first-order condition for a dynamic choice problem. It describes the evolution of economic variables along an optimal path. It is a necessary but not sufficient condition for a candidate optimal path, and so is useful for partially characterizing the theoretical implications of a range of models for dynamic beha...

We establish a result concerning the so-called Lagrangian controllability of the Euler equation for incompressible perfect fluids in dimension 3. More precisely we consider a connected bounded domain of R and two smooth contractible sets of fluid particles, surrounding the same volume. We prove that given any initial velocity field, one can find a boundary control and a time interval such that ...

In this paper we exploit the specific structure of the Euler equation and develop two alternative GMM estimators that deal explicitly with measurement error. The first estimator assumes that the measurement error is lognormally distributed. The second estimator drops the distributional assumption and solves out for the unknown, but constant, conditional mean. Our monte carlo results suggest tha...

The scalar nonconvex variational problems of the minimum-energy type on Sobolev spaces are studied. As the Euler-Lagrange equation dramatically looses selectivity when extended in terms of the Young measures, the correct optimality conditions are sought by means of the convex compactification theory. It turns out that these conditions basically combine one part from the Euler-Lagrange equation ...

In 1940 (and 1964) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1992 and 2008, J. M. Rassias introduced the Euler-Lagrange quadratic mappings and the JMRassias “product-sum” stability, respectively. In this paper we introduce an Euler-Lagrange type quadratic functional equation and investigate the JMRassias ...

A phenomenological two-fluid model of the (time-reversible) spectrally-truncated 3D Euler equation is proposed. The thermalized small scales are first shown to be quasi-normal. The effective viscosity and thermal diffusion are then determined, using EDQNM closure and Monte-Carlo numerical computations. Finally, the model is validated by comparing its dynamics with that of the original truncated...

The semi-geostrophic equations are used in meteorology. They appear as a variant of the two-dimensional Euler incompressible equations in vorticity form, where the Poisson equation that relates the stream function and the vorticity field is just replaced by the fully non linear elliptic Monge-Ampère equation. This work gathers new results concerning the semi-geostrophic equations: Existence and...