Enrique A. Thomann

Occupation and local times for skew Brownian motion with applications to dispersion across an interface

This research was partially supported by the grant GrantCMG EAR-0724865 from the National Science Foundation.

Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations

A general method is developed to obtain conditions on initial data and forcing terms for the global existence of unique regular solutions to incompressible 3d Navier-Stokes equations. The basic idea generalizes a probabilistic approach introduced by LeJan and Sznitman (1997) to obtain weak solutions whose Fourier transform may be represented by an expected value of a stochastic cascade. A functional analytic framework is also developed which partially connects stochastic iterations and certain Picard iterates. Some local existence and uniqueness results are also obtained by contractive mapping conditions on the Picard iteration.

The diffusion limit of free molecular flow in thin plane channels

The subject of this paper is free molecular flow in thin channels bounded by parallel plane surfaces on which Maxwell’s boundary condition applies. With tools from probability theory, it is proved that in the limit as the domain width h tends to zero, the evolution of the density is described by a diffusion equation, on a timescale of

A Generalized Taylor–Aris Formula and Skew Diffusion

1/(h\log h^{-1} )

Advection–Dispersion Across Interfaces

, and with a diffusion coefficient of

A note on the distribution of integrals of geometric Brownian motion

(2 - \alpha )\sqrt T /(2\alpha \sqrt \pi )

Singular vortex systems and weak solutions of the Euler equations

(

Operator Splitting for Navier-Stokes and Chorin-Marsden Product Formula

\alpha

Influences of fire–vegetation feedbacks and post‐fire recovery rates on forest landscape vulnerability to altered fire regimes

is the accommodation coefficient and T is the surface temperature). The logarithmic factor in the timescale is geometry dependent; in thin cylinders of diameter h, the timescale is

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

1/h