Mathematical Vindications of the "Jeans Swindle"
Michael K.-H. Kiessling
TL;DR
This paper rigorously justifies the Jeans dispersion relation and instability criterion through well-defined limiting procedures, clarifying the mathematical basis and vindicating the so-called 'Jeans swindle.'
Contribution
It provides a rigorous mathematical derivation of the Jeans instability criterion, clarifying the physical reasoning behind it and validating the original approach.
Findings
The Jeans dispersion relation is derived through a mathematically rigorous limiting process.
A second independent derivation confirms the validity of the Jeans instability criterion.
The work clarifies the mathematical and physical foundations of the Jeans swindle.
Abstract
The original Jeans dispersion relation and instability criterion are derived by a mathematically well-defined limiting procedure. The procedure highlights Jeans' physical reasoning and vindicates the (in)famous ``Jeans swindle.'' A second, independent procedure is stated which yields the same result.
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Taxonomy
TopicsFluid Dynamics and Turbulent Flows