Title

Analysis of the Navier--Stokes-αβ equations

Author

Joshua John Brady, Washington University in St. LouisFollow

Author's School

Graduate School of Arts & Sciences

Author's Department/Program

Mathematics

Language

English (en)

Date of Award

5-24-2012

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Renato Feres

Abstract

In this dissertation we prove various analytic results for the Navier--Stokes-αβ equations. We establish well-posedness and regularity. In addition we determine estimates for the nodal distance and the number of determining modes. A method of averaging is developed and applied to derive a Kaman--Howarth type equation for the Navier--Stokes-αβ equations. Finally we investigate an anisotropic generalization of the Navier--Stokes-αβ equations. We show that the eigenvalues of the moment of inertia tensor convect with the flow and we derive energy type inequalities for the equations.

Comments

Permanent URL: http://dx.doi.org/10.7936/K73776TG

Recommended Citation

Brady, Joshua John, "Analysis of the Navier--Stokes-αβ equations" (2012). All Theses and Dissertations (ETDs). 943.
https://openscholarship.wustl.edu/etd/943