Related papers: Jump problem for generalized Lam\'e-Navier systems…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
We study the Hankel determinant generated by the Laguerre weight with jump discontinuities at $t_k, k=1,\cdots,m$. By employing the ladder operator approach to establish Riccati equations, we show that $\sigma_n(t_1,\cdots,t_m)$, the…
We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the…
The concept of continuous topological evolution, based upon Cartan's methods of exterior differential systems, is used to develop a topological theory of non-equilibrium thermodynamics, within which there exist processes that exhibit…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…
We describe generalized Brownian motion related to parabolic equation systems from a logical point of view, i.e., as a generalization of Anderson's random walk. The connection to classical spaces is based on the Loeb measure. It seems that…
We consider the Cauchy problem in the band $\mathbb{C}^{n}\times[0, T], n>1,T>0$, for a system of nonlinear differential equations structurally similar to the classical Navier-Stokes equations for an incompressible fluid. The main…
We propose a two-dimensional generalization of Constantin-Lax-Majda model [2]. Some results about singular solutions are given. This model might be the first step toward the singular solutions of the Euler equations. Along the same line…
The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials…
In this work, a spin $\frac 12$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators…
In this paper, we study a hyperbolic version of the Navier-Stokes equations, obtained by using the approximation by relaxation of the Euler system, evolving in a thin strip domain. The formal limit of these equations is a hyperbolic Prandtl…
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…
We recover the Navier-Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on a higher-dimensional Euclidean space. We solve this problem…
This paper studies the global well-posedness of classical solutions to the isentropic compressible Navier-Stokes equations in 3D domains D under non-slip boundary conditions. D will separate into the inner and boundary parts along a free…
In calculus of variations on general time scales, an integral Euler-Lagrange equation is usually derived in order to characterize the critical points of non shifted Lagrangian functionals, see e.g. [R.A.C. Ferreira and co-authors,…
In this paper, we study the existence of solutions to the scalar additive Jump problem and the Riemann boundary value problems in the context of vectorial Clifford analysis on domains with fractal boundaries. A reduction procedure is…
In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top…