Izosimov, Anton; Khesin, Boris Geometry of generalized fluid flows. (English) Zbl 07782494 Calc. Var. Partial Differ. Equ. 63, No. 1, Paper No. 3, 30 p. (2024). MSC: 35Q31 37K30 58H05 76A02 76T30 PDFBibTeX XMLCite \textit{A. Izosimov} and \textit{B. Khesin}, Calc. Var. Partial Differ. Equ. 63, No. 1, Paper No. 3, 30 p. (2024; Zbl 07782494) Full Text: DOI arXiv
Khesin, Boris; Modin, Klas The Toda flow as a porous medium equation. (English) Zbl 07707364 Commun. Math. Phys. 401, No. 2, 1879-1898 (2023). MSC: 37K10 37K25 37J35 76B03 76D03 PDFBibTeX XMLCite \textit{B. Khesin} and \textit{K. Modin}, Commun. Math. Phys. 401, No. 2, 1879--1898 (2023; Zbl 07707364) Full Text: DOI arXiv
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
Khesin, Boris; Wang, Hanchun The golden ratio and hydrodynamics. (English) Zbl 07609240 Math. Intell. 44, No. 1, 22-27 (2022). MSC: 76-XX PDFBibTeX XMLCite \textit{B. Khesin} and \textit{H. Wang}, Math. Intell. 44, No. 1, 22--27 (2022; Zbl 07609240) Full Text: DOI arXiv
Khesin, Boris; Peralta-Salas, Daniel; Yang, Cheng A basis of Casimirs in 3D magnetohydrodynamics. (English) Zbl 1490.76238 Int. Math. Res. Not. 2021, No. 18, 13645-13660 (2021). MSC: 76W05 22E70 58J90 PDFBibTeX XMLCite \textit{B. Khesin} et al., Int. Math. Res. Not. 2021, No. 18, 13645--13660 (2021; Zbl 1490.76238) Full Text: DOI arXiv
Khesin, Boris; Misiołek, Gerard; Modin, Klas Geometric hydrodynamics and infinite-dimensional Newton’s equations. (English) Zbl 1473.35444 Bull. Am. Math. Soc., New Ser. 58, No. 3, 377-442 (2021). MSC: 35Q35 76A02 76-02 58B20 37K65 PDFBibTeX XMLCite \textit{B. Khesin} et al., Bull. Am. Math. Soc., New Ser. 58, No. 3, 377--442 (2021; Zbl 1473.35444) Full Text: DOI arXiv
Arnold, Vladimir I.; Khesin, Boris A. Topological methods in hydrodynamics. 2nd edition. (English) Zbl 1475.76003 Applied Mathematical Sciences 125. Cham: Springer (ISBN 978-3-030-74277-5/hbk; 978-3-030-74280-5/pbk; 978-3-030-74278-2/ebook). xx, 455 p. (2021). MSC: 76-02 76B47 76W05 58D30 PDFBibTeX XMLCite \textit{V. I. Arnold} and \textit{B. A. Khesin}, Topological methods in hydrodynamics. 2nd edition. Cham: Springer (2021; Zbl 1475.76003) Full Text: DOI
Khesin, Boris; Yang, Cheng Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations. (English) Zbl 1459.76032 Nonlinearity 34, No. 3, 1525-1542 (2021). MSC: 76B47 35Q51 37N10 PDFBibTeX XMLCite \textit{B. Khesin} and \textit{C. Yang}, Nonlinearity 34, No. 3, 1525--1542 (2021; Zbl 1459.76032) Full Text: DOI arXiv
Khesin, Boris; Misiolek, Gerard; Modin, Klas Geometric hydrodynamics via Madelung transform. (English) Zbl 1416.58006 Proc. Natl. Acad. Sci. USA 115, No. 24, 6165-6170 (2018). MSC: 58D30 58D05 60B99 76N10 37N10 PDFBibTeX XMLCite \textit{B. Khesin} et al., Proc. Natl. Acad. Sci. USA 115, No. 24, 6165--6170 (2018; Zbl 1416.58006) 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
Izosimov, Anton; Khesin, Boris Classification of Casimirs in 2D hydrodynamics. (English) Zbl 1415.76518 Mosc. Math. J. 17, No. 4, 699-716 (2017). MSC: 76M60 76A02 58B25 35Q31 PDFBibTeX XMLCite \textit{A. Izosimov} and \textit{B. Khesin}, Mosc. Math. J. 17, No. 4, 699--716 (2017; Zbl 1415.76518) Full Text: arXiv Link
Izosimov, Anton; Khesin, Boris Characterization of steady solutions to the 2D Euler equation. (English) Zbl 1405.35151 Int. Math. Res. Not. 2017, No. 24, 7459-7503 (2017). MSC: 35Q31 76B03 PDFBibTeX XMLCite \textit{A. Izosimov} and \textit{B. Khesin}, Int. Math. Res. Not. 2017, No. 24, 7459--7503 (2017; Zbl 1405.35151) Full Text: DOI arXiv
Izosimov, Anton; Khesin, Boris; Mousavi, Mehdi Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics. (Orbites coadjointes des difféomorphismes symplectiques des surfaces et hydrodynamique idéale.) (English. French summary) Zbl 1372.37106 Ann. Inst. Fourier 66, No. 6, 2385-2433 (2016). Reviewer: Marco Modugno (Firenze) MSC: 37J05 76M60 70G45 37N10 53D35 PDFBibTeX XMLCite \textit{A. Izosimov} et al., Ann. Inst. Fourier 66, No. 6, 2385--2433 (2016; Zbl 1372.37106) 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
Khesin, Boris Dynamics of symplectic fluids and point vortices. (English) Zbl 1307.76008 Geom. Funct. Anal. 22, No. 5, 1444-1459 (2012). MSC: 76B03 37N10 PDFBibTeX XMLCite \textit{B. Khesin}, Geom. Funct. Anal. 22, No. 5, 1444--1459 (2012; Zbl 1307.76008) Full Text: DOI arXiv
Khesin, Boris The group and Hamiltonian descriptions of hydrodynamical systems. (English) Zbl 1305.76025 Ricca, Renzo L. (ed.), Lectures on topological fluid mechanics. Lectures given at the C.I.M.E. summer school, Cetraro, Italy, July 2–10, 2001. Berlin: Springer (ISBN 978-3-642-00836-8/pbk; 978-3-642-00837-5/ebook). Lecture Notes in Mathematics 1973, 139-155 (2009). MSC: 76B99 58D30 35Q51 70H05 70G65 PDFBibTeX XMLCite \textit{B. Khesin}, Lect. Notes Math. 1973, 139--155 (2009; Zbl 1305.76025) Full Text: DOI
Khesin, Boris; Lee, Paul Poisson geometry and first integrals of geostrophic equations. (English) Zbl 1143.76413 Physica D 237, No. 14-17, 2072-2077 (2008). MSC: 76B99 37N10 53D17 PDFBibTeX XMLCite \textit{B. Khesin} and \textit{P. Lee}, Physica D 237, No. 14--17, 2072--2077 (2008; Zbl 1143.76413) Full Text: DOI arXiv
Khesin, Boris Groups and topology in the Euler hydrodynamics and KdV. (English) Zbl 1185.76446 Craig, Walter (ed.), Hamiltonian dynamical systems and applications. Proceedings of the NATO Advanced Study Institute on Hamiltonian dynamical systems and applications, Montreal, Canada, June, 18-29, 2007. Berlin: Springer (ISBN 978-1-4020-6963-5/pbk; 978-1-4020-6962-8/hbk). NATO Science for Peace and Security Series B: Physics and Biophysics, 93-102 (2008). Reviewer: Peter M. Akhmet’ev (Troitsk) MSC: 76B03 35Q35 35Q53 22E70 PDFBibTeX XMLCite \textit{B. Khesin}, in: Hamiltonian dynamical systems and applications. Proceedings of the NATO Advanced Study Institute on Hamiltonian dynamical systems and applications, Montreal, Canada, June, 18-29, 2007. Berlin: Springer. 93--102 (2008; Zbl 1185.76446)
Khesin, B.; Misiołek, G. Shock waves for the Burgers equation and curvatures of diffeomorphism groups. (English) Zbl 1161.35464 Proc. Steklov Inst. Math. 259, 73-81 (2007) and Tr. Mat. Inst. Steklova 259 (2007). MSC: 35Q35 58D05 58E10 76E17 PDFBibTeX XMLCite \textit{B. Khesin} and \textit{G. Misiołek}, Proc. Steklov Inst. Math. 259, 73--81 (2007; Zbl 1161.35464) Full Text: DOI arXiv
Khesin, Boris; Misiołek, Gerard Asymptotic directions, Monge-Ampère equations and the geometry of diffeomorphism groups. (English) Zbl 1081.76011 J. Math. Fluid Mech. 7, Suppl. 3, S365-S375 (2005). MSC: 76B03 58D30 PDFBibTeX XMLCite \textit{B. Khesin} and \textit{G. Misiołek}, J. Math. Fluid Mech. 7, S365--S375 (2005; Zbl 1081.76011) Full Text: DOI arXiv
Khesin, Boris Topological Fluid Dynamics. (English) Zbl 1078.37048 Notices Am. Math. Soc. 52, No. 1, 9-19 (2005). MSC: 37N10 37K65 57M60 58D05 76B99 86A10 PDFBibTeX XMLCite \textit{B. Khesin}, Notices Am. Math. Soc. 52, No. 1, 9--19 (2005; Zbl 1078.37048) Full Text: Link
Khesin, Boris A.; Michor, Peter W. The flow completion of the Burgers equation. (English) Zbl 1062.37100 Wurzbacher, Tilmann (ed.), Infinite dimensional groups and manifolds. Based on the 70th meeting of theoretical physicists and mathematicians at IRMA, Strasbourg, France, May 2004. Berlin: de Gruyter (ISBN 3-11-018186-X/pbk). IRMA Lectures in Mathematics and Theoretical Physics 5, 17-26 (2004). MSC: 37K65 35Q53 37N10 58D25 76D05 PDFBibTeX XMLCite \textit{B. A. Khesin} and \textit{P. W. Michor}, IRMA Lect. Math. Theor. Phys. 5, 17--26 (2004; Zbl 1062.37100)
Khesin, Boris Geometry in fluid motion. (English) Zbl 1056.37096 Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 2002-2003, Exp. No. X, 10 p. (2003). MSC: 37N10 35Q35 37K65 57M25 76M99 76W05 PDFBibTeX XMLCite \textit{B. Khesin}, Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau 2002--2003, Exp. No. X, 10 p. (2003; Zbl 1056.37096) Full Text: Numdam EuDML
Khesin, Boris A. Geometry of higher helicities. (English) Zbl 1156.55300 Mosc. Math. J. 3, No. 3, 989-1011 (2003). MSC: 55Q25 37A15 57M27 57R30 76W05 PDFBibTeX XMLCite \textit{B. A. Khesin}, Mosc. Math. J. 3, No. 3, 989--1011 (2003; Zbl 1156.55300) Full Text: Link
Khesin, Boris A. Topology bounds the energy. (English) Zbl 1210.58017 Ricca, Renzo L. (ed.), An introduction to the geometry and topology of fluid flows. Proceedings of the NATO Advanced Study Institute “Pedagogical workshop on geometry and topology of fluid flows”, Cambridge, UK, September 11–22, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0206-8/hbk). NATO Sci. Ser. II, Math. Phys. Chem. 47, 229-238 (2001). MSC: 58E50 76W05 PDFBibTeX XMLCite \textit{B. A. Khesin}, NATO Sci. Ser. II, Math. Phys. Chem. 47, 229--238 (2001; Zbl 1210.58017) Full Text: DOI
Arnold, V. I.; Khesin, B. A. Topological methods in hydrodynamics. (English) Zbl 0902.76001 Applied Mathematical Sciences. 125. New York, NY: Springer. xv, 374 p. (1998). Reviewer: F.Kaplanski (Tallinn) MSC: 76-02 76B47 76W05 58D30 PDFBibTeX XMLCite \textit{V. I. Arnold} and \textit{B. A. Khesin}, Topological methods in hydrodynamics. New York, NY: Springer (1998; Zbl 0902.76001)
Ginzburg, Viktor L.; Khesin, Boris Steady fluid flows and symplectic geometry. (English) Zbl 0805.58023 J. Geom. Phys. 14, No. 2, 195-210 (1994). MSC: 37J99 58E05 76B47 PDFBibTeX XMLCite \textit{V. L. Ginzburg} and \textit{B. Khesin}, J. Geom. Phys. 14, No. 2, 195--210 (1994; Zbl 0805.58023) Full Text: DOI
Arnold, V. I.; Khesin, B. A. Topological methods in hydrodynamics. (English) Zbl 0743.76019 Lumley, John L. (ed.) et al., Annual review of fluid mechanics. Vol. 24. Palo Alto, CA: Annual Reviews Inc. (ISBN 0-8243-0724-0/hbk). Annu. Rev. Fluid Mech. 24, 145-166 (1992). MSC: 76B99 76-02 57S05 PDFBibTeX XMLCite \textit{V. I. Arnold} and \textit{B. A. Khesin}, Annu. Rev. Fluid Mech. 24, 145--166 (1992; Zbl 0743.76019)
Ginzburg, Viktor L.; Khesin, Boris Topology of steady fluid flows. (English) Zbl 0789.76014 Moffatt, H. K. (ed.) et al., Topological aspects of the dynamics of fluids and plasmas. Proceedings of the program of the Institute for Theoretical Physics, University of California at Santa Barbara, USA and of the NATO advanced research workshop on topological aspects of the dynamics of fluids and plasmas, University of California at Santa Barbara, USA, November 1-5, 1991. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. E, Appl. Sci. 218, 265-272 (1992). MSC: 76B47 58D30 PDFBibTeX XMLCite \textit{V. L. Ginzburg} and \textit{B. Khesin}, NATO ASI Ser., Ser. E, Appl. Sci. 218, 265--272 (1992; Zbl 0789.76014)
Khesin, B. A. Ergodic interpretation of integral hydrodynamic invariants. (English) Zbl 0742.57020 J. Geom. Phys. 9, No. 1, 101-110 (1992). MSC: 57R40 58A10 57R30 76B47 PDFBibTeX XMLCite \textit{B. A. Khesin}, J. Geom. Phys. 9, No. 1, 101--110 (1992; Zbl 0742.57020) Full Text: DOI
Khesin, B. A.; Chekanov, Yu. V. Invariants of the Euler equations for ideal or barotropic hydrodynamics and superconductivity in \(D\) dimensions. (English) Zbl 0820.58019 Physica D 40, No. 1, 119-131 (1989). MSC: 37J99 58J70 76A02 76B99 PDFBibTeX XMLCite \textit{B. A. Khesin} and \textit{Yu. V. Chekanov}, Physica D 40, No. 1, 119--131 (1989; Zbl 0820.58019) Full Text: DOI
Ovsienko, V. Yu.; Khesin, B. A.; Chekanov, Yu. V. Integrals of the Euler equations of multidimensional hydrodynamics and superconductivity. (English. Russian original) Zbl 0779.76103 J. Sov. Math. 59, No. 5, 1096-1101 (1992); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 172, 105-113 (1989). MSC: 76W05 76A02 PDFBibTeX XML Full Text: DOI
Ovsienko, V. Yu.; Khesin, B. A.; Chekanov, Yu. V. Integrals of Euler equations of multidimensional hydrodynamics and superconductivity. (Russian. English summary) Zbl 0691.76122 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 172, 105-113 (1989). MSC: 76W05 76A02 PDFBibTeX XML Full Text: EuDML