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2020 | OriginalPaper | Chapter

1. An Approach to the Primitive Equations for Oceanic and Atmospheric Dynamics by Evolution Equations

Authors : Matthias Hieber, Amru Hussein

Published in: Fluids Under Pressure

Publisher: Springer International Publishing

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Abstract

The primitive equations for oceanic and atmospheric dynamics are a fundamental model for many geophysical flows. In this chapter we present a summary of an approach to these equations based on the theory of evolution equations. In particular, we discuss the hydrostatic Stokes operator, well-posedness results in critical spaces within the L p(L q)-scale, within the scaling invariant space L ∞(L 1) for Neumann boundary conditions, and within the L ∞(L p) space for mixed boundary conditions and p > 3. In addition, we investigate real analyticity of solutions, convergence of the scaled Navier-Stokes equations to the primitive equations, and the existence of periodic solutions for large forces.

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Metadata
Title
An Approach to the Primitive Equations for Oceanic and Atmospheric Dynamics by Evolution Equations
Authors
Matthias Hieber
Amru Hussein
Copyright Year
2020
Book
Fluids Under Pressure

Print ISBN: 978-3-030-39638-1

Electronic ISBN: 978-3-030-39639-8

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-39639-8_1

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