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Initial-boundary value problems on the sphere

In: Application of Holomorphic Functions in Two and Higher Dimensions

Author

Listed:
  • Klaus Gürlebeck

    (Bauhaus-Universität Weimar)

  • Klaus Habetha

    (RWTH Aachen)

  • Wolfgang Sprößig

    (TU Bergakademie Freiberg)

Abstract

In this chapter, we consider classes of fluid flow problems on the sphere and in ball shells with given initial and boundary value conditions. We focus our attention on the corresponding Navier-Stokes equations and their linearizations – the socalled forecasting equations. Shallow water equations are rather similar to this set of equations, and we shall discuss them as well. The physical background of such type of equations is described, for instance, in the book “Turbulence in fluids” by M. LESIEUR [195]. For a better understanding, we will give a brief introduction to the corresponding physical problems. The main aim of the section is to construct a quaternionic operator calculus tailored to the above mentioned applications.

Suggested Citation

  • Klaus Gürlebeck & Klaus Habetha & Wolfgang Sprößig, 2016. "Initial-boundary value problems on the sphere," Springer Books, in: Application of Holomorphic Functions in Two and Higher Dimensions, chapter 0, pages 319-328, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0964-1_10
    DOI: 10.1007/978-3-0348-0964-1_10
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