Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler-Lagrange equations, culminating in a blow up analysis.

To understand the nature of turbulence, we select 2D Euler equation under periodic boundary condition as our primary example to study. 2D Navier-Stokes equation at high Reynolds number is regarded as a singularly perturbed 2D Euler equation. That is, we are interested in studying the zero viscosity limit problem. To begin an infinite dimensional dynamical system study, we consider a simple fixe...

The econometric implementation of rational addiction theory has been highly influenced by Becker, Grossman and Murphy (BGM). They specify an Euler equation where current consumption is determined by current price and past and future consumption. This model is claimed to be able to discriminate between rational addictive, myopic addictive, and non-addictive behavior. However, as demonstrated in ...

We develop a quasilinear theory of the 2D Euler equation and derive an integrodifferential equation for the evolution of the coarse-grained vorticity omega;(r,t). This equation respects all of the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive an H theorem for the Fermi...

A stochastic Euler equation is proposed, describing the motion of a particle density, forced by the random action of virtual photons in vacuum. After time averaging, the Euler equation is reduced to the Reynolds equation, well studied in turbulent hydrodynamics. It is shown that the average pressure is nonlocal and the magnitude of the turbulent flow obeys the Fick law. Using the Madelung trans...

ABSTRACT. We extend a recent result on third and fourth-order Cauchy-Euler equations by establishing the Hyers-Ulam stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there exists an exact solution to that dynamic equation that is close to the approximate one. We...

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function ...

A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems aris...

A form of the Euler equation using an impulse formulation is presented. This form is based on a representation of the divergence-free projection operator in terms of a continuous distribution of vortex dipoles which have a finite self-induced velocity. A generalization of the Euler equation is presented as a kinetic equation similar to the Vlasov–Poisson equation. An interesting feature of this...

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.