相关论文: The Inverse Problem for the Euler-Poisson system i…

We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…

The motion of a rolling ball actuated by internal point masses that move inside the ball's frame of reference is considered. The equations of motion are derived by applying Euler-Poincar\'e's symmetry reduction method in concert with…

Using the Hamiltonian formulation, we have attempted to obtain the equations of motion of systems with internal angular momentum that are moving with respect to a reference system when subjected to an interaction. This interaction involves…

We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill--posed in the class of weak solutions for a large class of physically admissible data.…

A exact de Sitter-like cosmological solution of quadratic gravitation with torsion has been found. In the limit of constant energy and pressure, it becomes a exact de Sitter spacetime. It exists in a wide class of quadratic gravity theories…

In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the…

A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way…

Equations of motion for a general relativistic post-Newtonian Lagrangian approach mainly refer to acceleration equations, i.e. differential equations of velocities. They are directly from the Euler-Lagrangian equations, and usually have…

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter…

A unified field theory for the description of matter in a curved space is discussed. The description is based on a standard Lagrangianian formalism in a pseudo-Euclidian 4D continuum using a 3-index tensor as independent variables. The…

The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…

The gravitational effect of vacuum polarization in space exterior to a particle in (2+1)-dimensional Einstein theory is investigated. In the weak field limit this gravitational field corresponds to an inverse square law of gravitational…

Proposed in this paper is a possible interaction which exists in nature - inertial interaction. It gives matter an inertia and inertial mass. The formula of inertial mass has been derived. It is possible that inertial interaction leads to…

The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…

After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…

The gravitational potential and the gravitational rotation field generated by a thin-disk mass distribution with exponential density are considered in the case when the force between any two mass elements is not the usual Newtonian one, but…

We consider the (barotropic) Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show that the initial value problem is ill-posed in the class of…

A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most…

We study four problems in the dynamics of a body moving about a fixed point, providing a non-complex, analytical solution for all of them. For the first two, we will work on the motion first integrals. For the symmetrical heavy body, that…

The basic aim is to extend some results and concepts of non-autonomous second order differential systems with convex potentials to the new context of multi-time Poisson-gradient PDE systems with convex potential. In this sense, we prove…