## 42 Citations

### Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus

- Mathematics
- 2008

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

- Mathematics
- 2007

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

- Mathematics
- 2004

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

- Mathematics
- 2008

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

- PhysicsJournal of Fluid Mechanics
- 2004

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

- Mathematics
- 2003

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

- Mathematics
- 2012

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

- Mathematics
- 2011

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.

- Mathematics
- 2011

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…