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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: Branching processes in Fluid Mechanics - An application to the Navier-Stokes and LANS-alpha equations

Workshop: Computational Methods with Applications in Finance, Insurance and the Life Sciences AND Stochastic Methods in Partial Differential Equations and Applications of Deterministic and Stochastic PDEs

Time: Thu, November 20, 2008, 10:50-11:40

Speaker: Enrique Thomann

Abstract

The Lagrangian Averaged Navier-Stokes (LANS-alpha) equations have been introduced for numerical purposes to approximate the Navier–Stokes equations at low Reynolds numbers.
Branching processes can be used to obtain a representation of solutions to these equations. The advantage of this representation is that the solutions are obtained as a multiplicative functional (which does not depend on the smoothing parameter alpha) and are defined in a common probability space.
Utilizing this representation, rates of convergence are obtained in a mixed spatio/temporal norm. The results presented in this talk represent work done in collaboration with Larry Chen, Ron Guenther, Ed Waymire from Oregon State University and Sun-Chul Kim from Chung Ang University.

Presentation slides (pdf, 4.6 MB)

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