Geometric investigations of a vorticity model equation
نویسندگان
چکیده
منابع مشابه
Geometric Investigations of a Vorticity Model Equation
This article consists of a detailed geometric study of the one-dimensional vorticity model equation ωt + uωx + 2ωux = 0, ω = Hux, t ∈ R, x ∈ S 1 , which is a particular case of the generalized Constantin-Lax-Majda equation. Wunsch showed that this equation is the Euler-Arnold equation on Diff(S) when the latter is endowed with the rightinvariant homogeneous Ḣ–metric. In this article we prove th...
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The geometry of a vorticity model equation
We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics [22] describes the geodesic flow on the subgroup Diff∞1 (S) of orientation-preserving diffeomorphisms φ ∈ Diff∞(S) such that φ(1) = 1 with respect to right-invariant metric induced by the homogeneous Sobolev space Ḣ(S) and show the local existence of the geodes...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2016
ISSN: 0022-0396
DOI: 10.1016/j.jde.2015.09.030