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An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations
Inviscid model, singularity explicit solutions 2D Boussinesq equations
2014/4/3
We give an example of a well posed, nite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce nite time sing...
Coupling solutions of BGG-equations in conformal spin geometry
overdetermined systems conformal spin geometry twistor spinors conformal Killing fields conformal Killing forms
2010/12/1
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and su...
Two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations
Camassa–Holm equation Degasperis–Procesi equation semidirect product geodesic flow
2010/11/26
We use geometric methods to study two natural two-component generalizations of the periodic Camassa–Holm and Degasperis–Procesi equations.