Abstract
This book contains results in three directions: the Thomas-Fermi regime or small ε problem, where there is a bounded number of vortices in the system (Chapters 3, 4, 6); the fast-rotation regime, which displays a vortex lattice (Chapter 5); and the experiment of a superfluid flow around an obstacle (Chapter 7). The tools and techniques needed to address these problems are very different: energy expansion using a small parameter for the Thomas-Fermi regime; double-scale convergence, homogenization techniques, and Fock-Bargmann space for the fast-rotating regime; energy estimates and nondegeneracy of a solution for the superfluid flow. The main mathematical results are summarized in the present chapter.
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© 2006 Birkhäuser Boston
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(2006). The Mathematical Setting: A Survey of the Main Theorems. In: Vortices in Bose—Einstein Condensates. Progress in Nonlinear Differential Equations and Their Applications, vol 67. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4492-X_2
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DOI: https://doi.org/10.1007/0-8176-4492-X_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4392-8
Online ISBN: 978-0-8176-4492-5
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