Summary
The Navier-Stokes equations for an incompressible viscous fluid admit time translation, time dependent change of the pressure origin, a scale change, rotation of axes, and time dependent spatial translation. No other transformations appear if dependence on derivatives is allowed.
Zusammenfassung
Die Navier-Stokes Gleichungen für ein inkompressibles, viskoses Fluid lassen eine Zeitverschiebung, eine zeitabhängige Verschiebung des Druckursprungs, eine Maßstabsänderung, eine Verdrehung der Achsen und eine zeitabhängige, räumliche Verschiebung zu. Andere Transformationen erscheinen nicht, wenn eine Abhängigkeit von den Ableitungen zugelassen wird.
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References
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This work was supported by the Office of Naval Research, Code 480.
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Lloyd, S.P. The infinitesimal group of the Navier-Stokes equations. Acta Mechanica 38, 85–98 (1981). https://doi.org/10.1007/BF01351464
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DOI: https://doi.org/10.1007/BF01351464