Governing equations of motion for a viscous incompressible material surface are derived
from the balance laws of continuum mechanics. The surface is treated as a time-dependent …

In this paper we study parametric trace finite element (TraceFEM) and parametric surface
finite element (SFEM) discretizations of a surface Stokes problem. These methods are …

Since Kolmogorov's theory, turbulence has been studied using various methods, many of
which could be now be understood in a probabilistic framework. Herein, a comprehensive …

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the
deterministic Navier–Stokes equation is regarded as a mean time derivative taken over …

This paper considers the equations governing incompressible fluid-flow on an evolving
surface. We employ an energetic variational approach to derive the dynamical system for the …

We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The
equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid …

We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating
noise and dissipation into mechanical systems arising from the theory of reduction by …

We prove a Euler-Poincaré reduction theorem for stochastic processes taking values on a
Lie group, which is a generalization of the reduction argument for the deterministic case [JE …

We consider the motion of an incompressible viscous fluid that completely covers a smooth,
compact and embedded hypersurface Σ Σ without boundary and flows along Σ Σ. Local-in …

In this paper we present a derivation of the surface Helmholtz decomposition, discuss its
relation to the surface Hodge decomposition and derive a well-posed stream function …