Khesin, Boris; Misiołek, Gerard; Shnirelman, Alexander Geometric hydrodynamics in open problems. (English) Zbl 1509.35198 Arch. Ration. Mech. Anal. 247, No. 2, Paper No. 15, 43 p. (2023). MSC: 35Q31 35Q35 76-02 76B03 76N10 76U60 58D05 35A15 35A20 35A21 35A01 35A02 35B41 35B65 PDFBibTeX XMLCite \textit{B. Khesin} et al., Arch. Ration. Mech. Anal. 247, No. 2, Paper No. 15, 43 p. (2023; Zbl 1509.35198) Full Text: DOI arXiv
Hochgerner, Simon Feedback control of charged ideal fluids. (English) Zbl 1459.76054 Nonlinearity 34, No. 3, 1316-1351 (2021). MSC: 76E25 76X05 93B52 93C20 37N10 PDFBibTeX XMLCite \textit{S. Hochgerner}, Nonlinearity 34, No. 3, 1316--1351 (2021; Zbl 1459.76054) Full Text: DOI arXiv
Arnaudon, Marc; Cruzeiro, Ana Bela; Léonard, Christian; Zambrini, Jean-Claude An entropic interpolation problem for incompressible viscous fluids. (English. French summary) Zbl 1458.76024 Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 3, 2211-2235 (2020). MSC: 76D03 76M30 49Q20 49S05 35Q35 PDFBibTeX XMLCite \textit{M. Arnaudon} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 3, 2211--2235 (2020; Zbl 1458.76024) Full Text: DOI arXiv Euclid
Voiculescu, Dan-Virgil A hydrodynamic exercise in free probability: setting up free Euler equations. (English) Zbl 1461.46066 Expo. Math. 38, No. 2, 271-283 (2020). MSC: 46L54 76B99 PDFBibTeX XMLCite \textit{D.-V. Voiculescu}, Expo. Math. 38, No. 2, 271--283 (2020; Zbl 1461.46066) Full Text: DOI arXiv
Blender, Richard Instability of planetary flows using Riemann curvature: a numerical study. (English) Zbl 1521.76028 Geophys. Astrophys. Fluid Dyn. 113, No. 5-6, 594-601 (2019). MSC: 76A02 53Z05 PDFBibTeX XMLCite \textit{R. Blender}, Geophys. Astrophys. Fluid Dyn. 113, No. 5--6, 594--601 (2019; Zbl 1521.76028) Full Text: DOI arXiv
Liu, Jian-Guo; Pego, Robert L.; Slepčev, Dejan Least action principles for incompressible flows and geodesics between shapes. (English) Zbl 1428.35376 Calc. Var. Partial Differ. Equ. 58, No. 5, Paper No. 179, 43 p. (2019). MSC: 35Q35 65D18 35J96 58E10 53C22 76B45 86A05 35R35 PDFBibTeX XMLCite \textit{J.-G. Liu} et al., Calc. Var. Partial Differ. Equ. 58, No. 5, Paper No. 179, 43 p. (2019; Zbl 1428.35376) Full Text: DOI arXiv
Izosimov, Anton; Khesin, Boris Vortex sheets and diffeomorphism groupoids. (English) Zbl 1442.76001 Adv. Math. 338, 447-501 (2018). MSC: 76-02 35Q31 53Z05 17B81 76B99 PDFBibTeX XMLCite \textit{A. Izosimov} and \textit{B. Khesin}, Adv. Math. 338, 447--501 (2018; Zbl 1442.76001) Full Text: DOI arXiv
Besse, Nicolas; Frisch, Uriel Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces. (English) Zbl 1374.76005 J. Fluid Mech. 825, 412-478 (2017). MSC: 76A02 76M30 76W05 17B81 22E70 PDFBibTeX XMLCite \textit{N. Besse} and \textit{U. Frisch}, J. Fluid Mech. 825, 412--478 (2017; Zbl 1374.76005) Full Text: DOI arXiv
Mérigot, Quentin; Mirebeau, Jean-Marie Minimal geodesics along volume-preserving maps, through semidiscrete optimal transport. (English) Zbl 1354.65136 SIAM J. Numer. Anal. 54, No. 6, 3465-3492 (2016). MSC: 65K10 49J20 49M25 PDFBibTeX XMLCite \textit{Q. Mérigot} and \textit{J.-M. Mirebeau}, SIAM J. Numer. Anal. 54, No. 6, 3465--3492 (2016; Zbl 1354.65136) Full Text: DOI arXiv
McOwen, Robert; Topalov, Peter Groups of asymptotic diffeomorphisms. (English) Zbl 1457.58008 Discrete Contin. Dyn. Syst. 36, No. 11, 6331-6377 (2016). MSC: 58D05 35Q31 76N10 PDFBibTeX XMLCite \textit{R. McOwen} and \textit{P. Topalov}, Discrete Contin. Dyn. Syst. 36, No. 11, 6331--6377 (2016; Zbl 1457.58008) Full Text: DOI arXiv
Boatto, Stefanella; Koiller, Jair Vortices on closed surfaces. (English) Zbl 1402.76034 Chang, Dong Eui (ed.) et al., Geometry, mechanics, and dynamics. The legacy of Jerry Marsden. Selected papers presented at a focus program, Fields Institute for Research in Mathematical Sciences, Toronto, Canada, July 2012. New York, NY: Springer (ISBN 978-1-4939-2440-0/hbk; 978-1-4939-2441-7/ebook). Fields Institute Communications 73, 185-237 (2015). MSC: 76B47 53D20 PDFBibTeX XMLCite \textit{S. Boatto} and \textit{J. Koiller}, Fields Inst. Commun. 73, 185--237 (2015; Zbl 1402.76034) Full Text: DOI arXiv
Bauer, Martin; Escher, Joachim; Kolev, Boris Local and global well-posedness of the fractional order EPDiff equation on \(\mathbb{R}^d\). (English) Zbl 1323.58007 J. Differ. Equations 258, No. 6, 2010-2053 (2015). Reviewer: Vagn Lundsgaard Hansen (Lyngby) MSC: 58D05 35Q35 35R11 PDFBibTeX XMLCite \textit{M. Bauer} et al., J. Differ. Equations 258, No. 6, 2010--2053 (2015; Zbl 1323.58007) Full Text: DOI arXiv
Arnold, Vladimir I. Givental, Alexander B. (ed.); Khesin, Boris A. (ed.); Varchenko, Alexander N. (ed.); Vassiliev, Victor A. (ed.); Viro, Oleg Ya. (ed.) Vladimir I. Arnold – Collected works. Vol. II. Hydrodynamics, bifurcation theory, and algebraic geometry 1965–1972. Edited by Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev and Oleg Ya. Viro. (English) Zbl 1354.01038 Berlin: Springer (ISBN 978-3-642-31030-0/hbk; 978-3-642-31031-7/ebook). xiii, 464 p. (2014). Reviewer: Gerard Misiołek (Notre Dame) MSC: 01A75 14-03 37-03 76-03 PDFBibTeX XMLCite \textit{V. I. Arnold} et al., Vladimir I. Arnold -- Collected works. Vol. II. Hydrodynamics, bifurcation theory, and algebraic geometry 1965--1972. Edited by Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev and Oleg Ya. Viro. Berlin: Springer (2014; Zbl 1354.01038) Full Text: DOI
Brandenbursky, Michael; Kȩdra, Jarek Quasi-isometric embeddings into diffeomorphism groups. (English) Zbl 1292.57029 Groups Geom. Dyn. 7, No. 3, 523-534 (2013). Reviewer: Vagn Lundsgaard Hansen (Lyngby) MSC: 57S05 20F65 PDFBibTeX XMLCite \textit{M. Brandenbursky} and \textit{J. Kȩdra}, Groups Geom. Dyn. 7, No. 3, 523--534 (2013; Zbl 1292.57029) Full Text: DOI arXiv
Arnaudon, Marc; Cruzeiro, Ana Bela Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability. (English) Zbl 1254.35174 Bull. Sci. Math. 136, No. 8, 857-881 (2012). MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{M. Arnaudon} and \textit{A. B. Cruzeiro}, Bull. Sci. Math. 136, No. 8, 857--881 (2012; Zbl 1254.35174) Full Text: DOI arXiv
Ebin, David G. Geodesics on the symplectomorphism group. (English) Zbl 1252.58006 Geom. Funct. Anal. 22, No. 1, 202-212 (2012). Reviewer: Renato G. Bettiol (Notre Dame) MSC: 58D05 53C22 53D05 53D25 53D35 58B10 58E10 PDFBibTeX XMLCite \textit{D. G. Ebin}, Geom. Funct. Anal. 22, No. 1, 202--212 (2012; Zbl 1252.58006) Full Text: DOI
Kohlmann, Martin A note on multi-dimensional Camassa-Holm-type systems on the torus. (English) Zbl 1239.58022 J. Phys. A, Math. Theor. 45, No. 12, Article ID 125205, 12 p. (2012). MSC: 58J99 58B25 35Q35 53D25 58D05 PDFBibTeX XMLCite \textit{M. Kohlmann}, J. Phys. A, Math. Theor. 45, No. 12, Article ID 125205, 12 p. (2012; Zbl 1239.58022) Full Text: DOI arXiv
Pommaret, J.-F. Arnold’s hydrodynamics revisited. (English) Zbl 1197.76014 Arab. J. Sci. Eng. (AJSE), Math. 1, No. 1, 157-174 (2009). Reviewer: Alain Brillard (Riedisheim) MSC: 76A02 53Z05 22E70 PDFBibTeX XMLCite \textit{J. F. Pommaret}, Arab. J. Sci. Eng. (AJSE), Math. 34, No. 1D, 157--174 (2009; Zbl 1197.76014) Full Text: arXiv
Holm, Darryl D.; Schmah, Tanya; Stoica, Cristina Geometric mechanics and symmetry. From finite to infinite dimensions. (English) Zbl 1175.70001 Oxford Texts in Applied and Engineering Mathematics 12. Oxford: Oxford University Press (ISBN 978-0-19-921291-0/pbk; 978-0-19-921290-3/hbk). xvi, 515 p. (2009). Reviewer: Giuseppe Gaeta (Milano) MSC: 70-01 37-01 70G45 37J15 37Jxx 37K05 37K10 37N10 53D05 70G40 70G65 PDFBibTeX XMLCite \textit{D. D. Holm} et al., Geometric mechanics and symmetry. From finite to infinite dimensions. Oxford: Oxford University Press (2009; Zbl 1175.70001)
Smolentsev, N. K. Diffeomorphism groups of compact manifolds. (English. Russian original) Zbl 1147.58012 J. Math. Sci., New York 146, No. 6, 6213-6312 (2007); translation from Sovrem. Mat. Prilozh. 37, 3-100 (2006). Reviewer: Andrew Bucki (Edmond) MSC: 58D17 53D05 76A99 58-02 PDFBibTeX XMLCite \textit{N. K. Smolentsev}, J. Math. Sci., New York 146, No. 6, 6213--6312 (2007; Zbl 1147.58012); translation from Sovrem. Mat. Prilozh. 37, 3--100 (2006) Full Text: DOI
Gomes, Diogo Aguiar A variational formulation for the Navier-Stokes equation. (English) Zbl 1080.37083 Commun. Math. Phys. 257, No. 1, 227-234 (2005). MSC: 37K65 35Q30 76D05 37N10 76M30 93C20 PDFBibTeX XMLCite \textit{D. A. Gomes}, Commun. Math. Phys. 257, No. 1, 227--234 (2005; Zbl 1080.37083) Full Text: DOI
Haller, Stefan; Teichmann, Josef; Vizman, Cornelia Totally geodesic subgroups of diffeomorphisms. (English) Zbl 1004.58004 J. Geom. Phys. 42, No. 4, 342-354 (2002). Reviewer: Andrew Bucki (Oklahoma City) MSC: 58D05 58B20 37K65 PDFBibTeX XMLCite \textit{S. Haller} et al., J. Geom. Phys. 42, No. 4, 342--354 (2002; Zbl 1004.58004) Full Text: DOI arXiv
Szenthe, J. Existence of stationary geodesics of left-invariant Lagrangians. (English) Zbl 0990.53037 J. Phys. A, Math. Gen. 34, No. 1, 165-175 (2001). Reviewer: Pascual Lucas Saorín (Murcia) MSC: 53C22 53D25 70H03 PDFBibTeX XMLCite \textit{J. Szenthe}, J. Phys. A, Math. Gen. 34, No. 1, 165--175 (2001; Zbl 0990.53037) Full Text: DOI
Marsden, J. E.; Ratiu, T. S.; Shkoller, S. The geometry and analysis of the averaged Euler equations and a new diffeomorphism group. (English) Zbl 0979.58004 Geom. Funct. Anal. 10, No. 3, 582-599 (2000). Reviewer: Nicolai Konstantinovish Smolentsev (Kemerovo) MSC: 58D05 58D30 76D05 PDFBibTeX XMLCite \textit{J. E. Marsden} et al., Geom. Funct. Anal. 10, No. 3, 582--599 (2000; Zbl 0979.58004) Full Text: DOI arXiv
Chigirinskaya, Y.; Schertzer, D. Cascade of scaling gyroscopes: Lie structure, universal multifractals and self-organized criticality in turbulence. (English) Zbl 0866.60100 Molchanov, Stanislav A. (ed.) et al., Stochastic models in geosystems. Based on a workshop, held during the week of May 16, 1994 at IMA, Minneapolis, MN, USA. Berlin: Springer. IMA Vol. Math. Appl. 85, 57-81 (1997). MSC: 60K99 PDFBibTeX XMLCite \textit{Y. Chigirinskaya} and \textit{D. Schertzer}, IMA Vol. Math. Appl. 85, 57--81 (1997; Zbl 0866.60100)
Toth, John A. On a class of spherical harmonics associated with rigid body motion. (English) Zbl 0843.58072 Math. Res. Lett. 1, No. 2, 203-210 (1994). MSC: 37J35 37K10 33E10 70E15 70H99 PDFBibTeX XMLCite \textit{J. A. Toth}, Math. Res. Lett. 1, No. 2, 203--210 (1994; Zbl 0843.58072) Full Text: DOI
Lukatsky, Alexander M. On the curvature of the diffeomorphism group. (English) Zbl 0816.58009 Ann. Global Anal. Geom. 11, No. 2, 135-140 (1993). Reviewer: W.Mozgawa (Lublin) MSC: 58D05 53C21 PDFBibTeX XMLCite \textit{A. M. Lukatsky}, Ann. Global Anal. Geom. 11, No. 2, 135--140 (1993; Zbl 0816.58009) Full Text: DOI
Simo, J. C.; Posbergh, T. A.; Marsden, J. E. Stability of relative equilibria. II: Application to nonlinear elasticity. (English) Zbl 0738.70011 Arch. Ration. Mech. Anal. 115, No. 1, 61-100 (1991). Reviewer: Franco Cardin MSC: 70H33 74B20 PDFBibTeX XMLCite \textit{J. C. Simo} et al., Arch. Ration. Mech. Anal. 115, No. 1, 61--100 (1991; Zbl 0738.70011) Full Text: DOI