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Quantized vortices, travelling coherent structures and superfluid turbulence. (English) Zbl 1166.35360
Farina, Alberto (ed.) et al., Stationary and time dependent Gross-Pitaevskii equations. Wolfgang Pauli Institute 2006 thematic program, January–December, 2006, Vienna, Austria. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4357-4/pbk). Contemporary Mathematics 473, 27-54 (2008).
Summary: The Gross-Pitaevskii equation and its modifications are used to elucidate different aspects of superfluid behaviour; motion of vortices, travelling waves, interactions with normal fluid and superfluid turbulence. Different mechanisms of formation of travelling coherent structures are considered. They are formed when a critical velocity is exceeded in the flow. They can appear as a result of instabilities or energy transfer among waves. They are formed together with the formation of condensate, but the interactions with normal fluid (non-condensed particles) lead to their dissipation.
For the entire collection see [Zbl 1149.35002].

35Q35 PDEs in connection with fluid mechanics
76A25 Superfluids (classical aspects)
76F02 Fundamentals of turbulence