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Publications

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Ilin KI, Vladimirov VA.  2006.  Asymptotic model for free surface flow of an electrically conducting fluid in a high-frequency magnetic field. Journal of Computational and Applied Mathematics. 190:520-531. Abstract  Download: Iline_Vlad.JCAM_2006.pdf (194.57 KB)
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Ilin KI, Vladimirov VA.  2004.  Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation. Physics of Plasmas. 11:3586-3594. Abstract
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Vladimirov VA, Ilin KI.  1998.  Generalized Izovorticity Principle for Ideal Magnetohydrodynamics. Harlow: Longman. Pitman Res.Notes Math. Ser. 386:161-177.
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Vladimirov VA, Moffatt HK, Ilin KI.  1998.  Isomagnetic Conditions for three-dimensional flows. Preprint of the Isaac Newton Institute for Mathematical Sciences. NI98024-STA :1-24.
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Vladimirov VA, Ilin KI.  1998.  Note on the nonlinear stability of stratified fluid equilibria. PhysicaD. 118:123-133. Abstract  Download: Vlad-Ilin-1998.pdf (481.05 KB)
Vladimirov VA, Ilin KI.  1998.  Note on the three-dimensional stability of a steady magnetohydrodynamic flow of an ideal fluid. Physics of Plasmas (Physics of Fluids, B). 5(12):4199-4204.
Govorukhin VN, Ilin KI.  2009.  Numerical study of an inviscid incompressible flow through a channel of finite length. Internat. J. Numer. Methods Fluids . 60(12):1315--1333.
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Vladimirov VA, Ilin KI.  1999.  On Arnold’s Variational Principles in Fluid Mechanics. Fields Institute Commun. 24:471-495.
Vladimirov VA, Ilin KI.  1999.  On Arnold’s Variational Principles in Fluid Mechanics. Fields Institute Commun. 24:471-495.
Vladimirov VA, Moffatt HK, Ilin KI.  1996.  On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part II. Stability criteria, for two-dimensional flow. J. Fluid Mech. 329:187-205.
Vladimirov VA, Moffatt HK, Ilin KI.  1997.  On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part III. Stability criteria, for axisymmetric flows. J. Plasma Physics. 57(1):89-120.
Vladimirov VA, Moffatt HK, Ilin KI.  1999.  On General Transformations and Variational Principles for the Magnetohydrodynamics of Ideal Fluids. Part IV. Generalized Isovorticity Principle for Three-Dimensional Flows. J.Fluid Mech. 390:127-150.
Vladimirov VA, Mu-Mu, Wu-Yong-hui, Ilin KI.  1999.  On nonlinear stability of baroclinic fronts. J. of Geophysical and Astrophysical Fluid Dynamics. 91(1-2):65-84.
Vladimirov VA, Ilin KI.  1991.  On slow motion of a rigid body in a stratified fluid. J. Appl. Mech. Tech. Phys. 27(2):55-60.
Ilin KI, Trakhinin Y.  2009.  On stability of Alfvén discontinuities. Math. Methods Appl. Sci.. 32 (3):307--329.
Vladimirov VA, Ilin KI.  1998.  On the Arnold Stability of a Solid in a Plane Steady Flow of an Ideal Incompressible Fluid. Theor.Comput.Fluid Dyn. 10(1-4):425-437.
Vladimirov VA, Ilin KI.  1998.  On the Energy Instability of Liquid Crystals. European Journal of Applied Mathematics. 9(1):23-36.
Vladimirov VA, Ilin KI.  1999.  On the stability of a Dynamical System `Rigid Body+ Inviscid Fluid'. Variational Principles. J. Fluid Mech. 386:43-75.
Davidson PA, Ilin KI, Moffatt HK, Vladimirov VA.  2003.  On the stability of a rigid body in a magnetostatic equilibrium. European Journal of Mechanics. B. Fluids. 22:511--523. Abstract  Download: Vlad-Mof-2003.pdf (270.47 KB)
Vladimirov VA, Ilin KI.  1997.  On the Stability of a Rigid Body in an Inviscid Steady Rotational Flow. Bull. Hong Kong Math, Soc. 1(1):103-131.
Ilin KI, Trakhinin YL.  2006.  On the stability of Alfven discontinuity. Physics of Plasmas. 13:102101,8pp. Abstract
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Vladimirov VA, Ilin KI.  1994.  Stability of a Solid in a Vortex Flow of an Ideal Liquid. J.Appl.Mech.Tech.Phys. 35(1):83-91.
Ilin KI, Trakhinin YL, Vladimirov VA.  2003.  The stability of steady magnetohydrodynamic flows with current-vortex sheets. Physics of Plasmas. 10:2649--2658. Abstract
Ilin KI, Morgulis A.  2011.  Steady streaming between two vibrating planes at high Reynolds numbers.
Ilin KI.  2011.  Steady streaming in a channel with permeable walls.

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