Related papers: Notes on approaches for solving the Euler-Poisson …
In this paper, we consider the compressible Euler-Maxwell equations arising in semiconductor physics, which take the form of Euler equations for the conservation laws of mass density and current density for electrons, coupled to Maxwell's…
3D stochastic Euler equations with a special form of multiplicative noise are considered. A Constantin-Iyer type representation in Euler-Lagrangian form is given, based on stochastic characteristics. Local existence and uniqueness of…
Euler's three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem…
By the extension of the 3-dimensional analytical solutions of Goldreich and Weber "P. Goldreich and S. Weber, Homologously Collapsing Stellar Cores, Astrophys, J. 238, 991 (1980)" with adiabatic exponent gamma=4/3, to the (classical)…
We present a preliminary study of a new phenomena associated with the Euler-Poisson equations -- the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…
In the present paper, an analysis was performed on the torque-free motion of a rigid body, developing Euler's analytical solution and Poinsot's geometric solution. From mathematical formulations, the analytical solution for the time…
This work showcases level set estimates for weak solutions to the $p$-Poisson equation on a bounded domain, which we use to establish Lebesgue space inclusions for weak solutions. In particular we show that if $\Omega\subset\mathbb{R}^n$ is…
A rotating continuum of particles attracted to each other by gravity may be modeled by the Euler-Poisson system. The existence of solutions is a very classical problem. Here it is proven that a curve of solutions exists, parametrized by the…
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that…
This paper presents a study of the isosceles problem resulting by a perturbation of Euler's collinear solution under Newtonian gravitational attraction of three bodies in space. After the Hamiltonian was obtained, a circumference of…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson-Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson-Boltzmann equation is…
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…
We investigate the global well-posedness of the ionic Vlasov-Poisson-Boltzmann system which models the evolution of dilute collisional ions. This system distinguishes the electronic Vlasov-Poisson-Boltzmann system via an additional…
We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter…
We describe an Euler scheme to approximate solutions of L\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the…
In this paper we mainly investigate the initial value problem of the periodic Euler-Poincar\'e equations. We first present a new blow-up result to the system for a special class of smooth initial data by using the rotational invariant…
E30 in the Enestrom index. Translated from the Latin original "De formis radicum aequationum cuiusque ordinis coniectatio" (1733). For an equation of degree n, Euler wants to define a "resolvent equation" of degree n-1 whose roots are…