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- Topological methods in hydrodynamics by V. Arnold and B. Khesin
- Bull. Amer. Math. Soc. 60 (2023), 271-276
- Additional book information: Applied Mathematical Sciences, Vol. 125, Springer, Cham, Second edition edition, 2021, xx+455 pp., ISBN 978-3-030-74277-5
References
- V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 319–361 (French). MR 202082
- V. Arnold and L. Meshalkin, A.N. Kolmogorov’s Seminar on Selected Problems of Analysis (1958/1959), Uspekhi Mat. Nauk 15 (1960), 247–250.
- Garrett Birkhoff, Hydrodynamics. A Study in Logic, Fact, and Similitude, Princeton University Press, Princeton, NJ, 1950. MR 38180
- Alexandre J. Chorin and Jerrold E. Marsden, A mathematical introduction to fluid mechanics, 3rd ed., Texts in Applied Mathematics, vol. 4, Springer-Verlag, New York, 1993. MR 1218879, DOI 10.1007/978-1-4612-0883-9
- Peter Constantin, On the Euler equations of incompressible fluids, Bull. Amer. Math. Soc. (N.S.) 44 (2007), no. 4, 603–621. MR 2338368, DOI 10.1090/S0273-0979-07-01184-6
- T. Drivas and T. Elgindi, Singularity formation in the incompressible Euler equation in finite and infinite time, arXiv:2203.17221v1 [math.AP], 31 Mar 2022.
- David G. Ebin and Jerrold Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. (2) 92 (1970), 102–163. MR 271984, DOI 10.2307/1970699
- Richard S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 65–222. MR 656198, DOI 10.1090/S0273-0979-1982-15004-2
- B. Khesin, G. Misiołek and A. Shnirelman, Geometric hydrodynamics in open problems, arXiv:2205.01143v1 [math.DG], 2 May 2022.
- L. D. Landau and E. M. Lifshitz, Fluid mechanics, Course of Theoretical Physics, Vol. 6, Pergamon Press, London-Paris-Frankfurt; Addison-Wesley Publishing Company, Inc., Reading, MA, 1959. Translated from the Russian by J. B. Sykes and W. H. Reid. MR 108121
- Leon Lichtenstein, Grundlagen der Hydromechanik, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 30, Springer-Verlag, Berlin, 1968 (German). MR 228225
- Andrew J. Majda and Andrea L. Bertozzi, Vorticity and incompressible flow, Cambridge Texts in Applied Mathematics, vol. 27, Cambridge University Press, Cambridge, 2002. MR 1867882
- Carlo Marchioro and Mario Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Applied Mathematical Sciences, vol. 96, Springer-Verlag, New York, 1994. MR 1245492, DOI 10.1007/978-1-4612-4284-0
- C. Truesdell, The kinematics of vorticity, Indiana Univ. Publ. Sci. Ser, no. 19, Indiana University Press, Bloomington, IN, 1954. MR 75003
Reviewer information
- Reviewer: Gerard Misiołek
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- Email: gmisiole@nd.edu
Additional Information
- Journal: Bull. Amer. Math. Soc. 60 (2023), 271-276
- DOI: https://doi.org/10.1090/bull/1794
- Published electronically: January 19, 2023
- Review Copyright: © Copyright 2023 American Mathematical Society