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

2007/03/03 by Clayton Bjorland, Bjorland, Clayton
Mathematics · Physics and Astronomy · #35B40 #35K55 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #math.AP #msc:35B40 #msc:35K55

paper · pdf · doi:10.48550/arxiv.math/0703095

22 pages, submitted

arxiv created 2007/03/03 · openalex publication_date 2007/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 L¹ 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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