The Nonisotropic average Euler equations
S. Shkoller (UC Davis)
I will present a derivation of a new model of incompressible hydrodynamics,
called the nonisotropic averaged Euler equations, based on fuzzying-up the
Lagrangian flow map, and averaging a new hybrid Eulerian-Lagrangian
decomposition of the macroscopic velocity field. The new model is a coupled
system of equations for the macroscopic velocity field u which is accurate
down to some given length scale alpha and a symmetric fluctuation
tensor F. Upon solving for (u,F), one can then solve for a "corrector"
which improves the accuracy of the macroscopic velocity field to O(alpha^2).
Some well-posedness results will be given.
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