On an infinite-interval boundary-value problem in geophysics

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Abstract

We derive a model for arctic gyre flows in rotating spherical coordinates that can be formulated as planar elliptic boundary-value problem by means of the stereographic projection. Moreover, for flows that are uniform in the azimuthal direction, the model is transformed to an infinite-interval boundary-value problem for a second-order ordinary differential equation. We investigate the existence of solutions of the infinite-interval boundary-value problem in the physically most relevant setting of constant oceanic vorticity using an integral re-formulation of the problem that also opens up the possibility of pursuing investigations of more general oceanic vorticities.

Keywords

Boundary-value problem Second order equations Geophysical flows 

Mathematics Subject Classification

Primary 45G99 58J32 76B03 

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina

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