相关论文: On the global version of Euler-Lagrange equations
The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary…
For a complex analytic variety with an action of a finite group and for an invariant 1-form on it, we give an equivariant version (with values in the Burnside ring of the group) of the local Euler obstruction of the 1-form and describe its…
Any classical solution of the 2D incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all…
This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…
Using the asymmetric fractional calculus of variations, we derive a fractional Lagrangian variational formulation of the convection-diffusion equation in the special case of constant coefficients.
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
We introduce new tetrads that manifestly and covariantly diagonalize the stress-energy tensor for a perfect fluid with vorticity at every spacetime point. This new tetrad can be applied and introduce simplification in the analysis of…
The Covariant Canonical Gauge theory of Gravity (CCGG) is a gauge field formulation of gravity which a priori includes non-metricity and torsion. It extends the Lagrangian of Einstein's theory of general relativity by terms at least…
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the…
We introduce a Lagrangian which can be varied to give both the equation of motion and world-line deviations of spinning particles simultaneously.
We show that complete cotangent lifts of vector fields, their decomposition into vertical representative and holonomic part provide a geometrical framework underlying Eulerian equations of continuum mechanics. We discuss Euler equations for…
Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph…
We discuss a general definition of directional derivative of any tensor flow field and its practical applications in physics. It is shown that both Lagrangian and Eulerian descriptions as complementary types of flow field specifications…
We present a method of constructing perturbative equations of motion for the geometric background of any given tensorial field theory. Requiring invariance of the gravitational dynamics under spacetime diffeomorphisms leads to a PDE system…
We covariantly modify the Einstein-Hilbert action such that the modified action perturbatively resolves the flat rotational velocity curve of the spiral galaxies and gives rise to the Tully-Fisher relation, and dynamically generates the…
We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the Lagrangian framework. Almost no exact Lagrangian solutions exist in the literature prior to this…
The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler equations, the proof is based in Ito-Wentzell-Kunita formula and stochastic analysis techniques.…
Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid…
This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references…
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…