• Corpus ID: 122631310

Global Analysis in Mathematical Physics: Geometric and Stochastic Methods

  title={Global Analysis in Mathematical Physics: Geometric and Stochastic Methods},
  author={I︠u︡. E. Gliklikh and Viktor L. Ginzburg},

On the two-point boundary-value problem for equations of geodesics

For equations of “geodesic spray” type with continuous coefficients on a complete Riemannian manifold, some interrelations between certain geometric characteristics, the distance between points, and

On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

We investigate velocity hodograph inclusions for the case of right- hand sides satisfying upper Caratheodory conditions. As an applica- tion we obtain an existence theorem for a boundary value

The Navier-Stokes equations and forward-backward SDEs on the group of volume-preserving diffeomorphisms of a flat torus

We establish a connection between the strong solution to the spatially periodic Navier–Stokes equations and a solution to a system of forward-backward stochastic differential equations (FBSDEs) on

A diffuse-interface method for simulating two-phase flows of complex fluids

Two-phase systems of microstructured complex fluids are an important class of engineering materials. Their flow behaviour is interesting because of the coupling among three disparate length scales:

Martingale problem approach to the representations of the Navier-Stokes equations on smooth-boundary manifolds and semispace

We present the random representations for the Navier-Stokes vorticity equations for an incompressible fluid in a smooth manifold with smooth boundary and reflecting boundary conditions for the

Generalized Navier-Stokes flows

We introduce a notion of generalized Navier-Stokes flows on manifolds, that extends to the viscous case the one defined by Brenier. Their kinetic energy extends the kinetic energy for classical

Mean Derivatives in Linear Spaces

In this section we briefly describe some preliminary facts about mean derivatives. For details, see (Azarina and Gliklikh, 2007), (Gliklikh, 1996, 1997, 2005), (Nelson, 1967, 1985). This notion was

A stochastic-Lagrangian approach to the Navier-Stokes equations in domains with boundary.

In this paper we derive a probabilistic representation of the deterministic 3-dimensional Navier--Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial