Abstract
Following Ebin and Marsden (Ann Math 92(1):102–163, 1970) we provide a concise proof of the well-posedness of the equations of perfect fluid motion. We use a construction which casts the equations as an ordinary differential equation on a non-linear function space.
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Notes
- 1.
Alternatively we could avoid detailed calculation by noting that \([\mathop{\mathrm{\mathrm{div}}}\nolimits _{\eta },\nabla _{v}]_{\eta }z = -\frac{d} {dt}(\mathop{\mathrm{\mathrm{div}}}\nolimits _{\eta (t)})z\) which is smooth since \(\mathop{\mathrm{\mathrm{div}}}\nolimits _{\eta }\) is smooth in η.
References
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Ebin, D.G. (2015). Groups of Diffeomorphisms and Fluid Motion: Reprise. In: Chang, D., Holm, D., Patrick, G., Ratiu, T. (eds) Geometry, Mechanics, and Dynamics. Fields Institute Communications, vol 73. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2441-7_6
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DOI: https://doi.org/10.1007/978-1-4939-2441-7_6
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