Decay Asymptotics of the Viscous Camassa-Holm Equations in the Plane

Details Decay Asymptotics of the Viscous Camassa-Holm Equations in the Plane Decay Asymptotics of the Viscous Camassa-Holm Equations in the Plane

2007-03-03

arxiv.org/abs/math/0703095v1

Mathematics

Analysis of PDEs

22 pages, submitted

Scientific paper

We consider the vorticity formulation of the 2-D viscous Camassa-Holm equations in the whole space. We establish global existence for solutions corresponding to initial data in $L^1$ and describe the large time behavior of solutions with sufficiently small and localized initial data. We calculate the rate at which such solutions approach an ``un-filtered'' Oseen vortex by computing the rate at which the solution of a scaled vorticity problem approaches the solution to a corresponding linearized equation.

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