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Long memory Mori-Zwanzig models for the Euler equation
Applied Math| Speaker: | Panagiotis Stinis, Lawrence Berkeley Lab |
| Location: | 1147 MSB |
| Start time: | Fri, Nov 3 2006, 4:10PM |
Description
A long memory model for dimensional reduction, known as the t-model, is
derived through the Mori-Zwanzig formalism of irreversible statistical
mechanics. The model is applied to the estimation of the rate of decay of solutions
of the Burgers equation and of the Euler equations in two and three space dimensions.
In the Burgers case the model captures the rate of decay exactly.
For the Euler equations in two space dimensions, the model preserves
energy as it should. In three dimensions the result are consistent with
estimates that are generally believed but could not previously be
computed. If time permits, we will discuss briefly a hierarchy of
Mori-Zwanzig models in which the t-model is the first one.