245 citations · 388 across the 12 of their papers we have counts for
3 papers · 1 filter
Reduced Singular Solutions of EPDiff Equations on Manifolds with Symmetry
Darryl D. Holm, Jonathan Munn, Samuel N. Stechmann
The EPDiff equation governs geodesic flow on the diffeomorphisms with respect to a chosen metric, which is typically a Sobolev norm on the tangent space of vector fields. EPDiff ad…
On asymptotically equivalent shallow water wave equations
H. R. Dullin, G. A. Gottwald, D. D. Holm
The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic…
Commutator-errors in large-eddy simulation
Bernard J. Geurts, Darryl D. Holm
A new formulation is derived for the commutator-errors in large-eddy simulation of incompressible flow. These commutator-errors arise from the application of non-uniform filters to…