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Stability and bifurcation of a viscous incompressible plasma fluid contained between two concentric rotating cylinders
1. | Department of Mathematics, Sichuan University, Chengdu, Sichuan 610021, China |
References:
[1] |
S. Chandrasekhar, Hydrodynamic and hydromagnetic Stability, The International Series of Monographs on Physics Clarendon Press, Oxford, 1961. xix+654 pp. (16 plates). |
[2] |
D. Biskamp, Nonlinear Magnetohydrodynamics, Cambridge University Press, Cambridge, 1993.
doi: 10.1017/CBO9780511599965. |
[3] |
P. Drazin and W. Reid, Hydrodynamic Stability, Cambridge University Press, 1981. |
[4] |
C. Foias, O. Manley and R. Temam, Attractors for the Bénard problem: existence and physical bounds on their fractal dimension, Nonlinear Anal, 11 (1987), no.8, 939-967.
doi: 10.1016/0362-546X(87)90061-7. |
[5] |
D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, 840. Springer-Verlag, Berlin-New York, 1981. iv+348 pp. ISBN: 3-540-10557-3 |
[6] |
V. I. Iudovich, Secondary flows and fluid instability between rotating cylinders, Prikl. Mat. Meh., 30 688-698 (Russian); translated as J. Appl. Math. Mech. 30 (1966), 822-833.
doi: 10.1016/0021-8928(66)90033-5. |
[7] |
K. Kirchg$\ddota$ssner, Bifurcation in nonlinear hydrodynamic stability, SIAM Rev., 17 (1975), 652-683.
doi: 10.1137/1017072. |
[8] |
R. Moreau, Magnetohydrodynamics, Kluwer Academic Publishers, Dordrecht, 1990. |
[9] |
T. Ma and S. Wang, Structural classification and stability of divergence-free vector fields, Phys. D, 171 (2002), 107-126.
doi: 10.1016/S0167-2789(02)00587-0. |
[10] |
T. Ma and S. Wang, Stability and bifurcation of the Taylor problem, Arch. Ration. Mech. Anal., 181 (2006), 149-176.
doi: 10.1007/s00205-006-0415-8. |
[11] |
T. Ma and S. Wang, Bifurcation Theory and Applications, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 53. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. xiv+375 pp. ISBN: 981-256-287-7
doi: 10.1142/9789812701152. |
[12] |
T. Ma and S. Wang, Geometric theory of incompressible flows with applications to fluid dynamics, Mathematical Surveys and Monographs, 119. American Mathematical Society, Providence, RI, 2005. x+234 pp. ISBN: 0-8218-3693-5 |
[13] |
T. Ma and S. Wang, Stability and Bifurcation of Nolinear Evolution Equations, Science Press, Beijing, 2007. |
[14] |
R. V. Polovin and V. P. Demutskii, Fundamentals of Magnetohydrodynamics, Consultants Bureau, New York, 1990. |
[15] |
G. I. Taylor, Stability of a viscous liquid contained between two rotating cyinders,, Phil. Trans. Roy. Soc. Lond. A, 223 (): 289.
|
[16] |
W. Velte, Stabilit$\ddota$t and verzweigung station$\ddotarer$ l$\ddot{0}$sungen der davier-stokeschen gleichungen beim Taylorproblem, Arch. Ration. Mech. Anal., 22 (1966), 1-14.
doi: 10.1007/BF00281240. |
show all references
References:
[1] |
S. Chandrasekhar, Hydrodynamic and hydromagnetic Stability, The International Series of Monographs on Physics Clarendon Press, Oxford, 1961. xix+654 pp. (16 plates). |
[2] |
D. Biskamp, Nonlinear Magnetohydrodynamics, Cambridge University Press, Cambridge, 1993.
doi: 10.1017/CBO9780511599965. |
[3] |
P. Drazin and W. Reid, Hydrodynamic Stability, Cambridge University Press, 1981. |
[4] |
C. Foias, O. Manley and R. Temam, Attractors for the Bénard problem: existence and physical bounds on their fractal dimension, Nonlinear Anal, 11 (1987), no.8, 939-967.
doi: 10.1016/0362-546X(87)90061-7. |
[5] |
D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, 840. Springer-Verlag, Berlin-New York, 1981. iv+348 pp. ISBN: 3-540-10557-3 |
[6] |
V. I. Iudovich, Secondary flows and fluid instability between rotating cylinders, Prikl. Mat. Meh., 30 688-698 (Russian); translated as J. Appl. Math. Mech. 30 (1966), 822-833.
doi: 10.1016/0021-8928(66)90033-5. |
[7] |
K. Kirchg$\ddota$ssner, Bifurcation in nonlinear hydrodynamic stability, SIAM Rev., 17 (1975), 652-683.
doi: 10.1137/1017072. |
[8] |
R. Moreau, Magnetohydrodynamics, Kluwer Academic Publishers, Dordrecht, 1990. |
[9] |
T. Ma and S. Wang, Structural classification and stability of divergence-free vector fields, Phys. D, 171 (2002), 107-126.
doi: 10.1016/S0167-2789(02)00587-0. |
[10] |
T. Ma and S. Wang, Stability and bifurcation of the Taylor problem, Arch. Ration. Mech. Anal., 181 (2006), 149-176.
doi: 10.1007/s00205-006-0415-8. |
[11] |
T. Ma and S. Wang, Bifurcation Theory and Applications, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 53. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. xiv+375 pp. ISBN: 981-256-287-7
doi: 10.1142/9789812701152. |
[12] |
T. Ma and S. Wang, Geometric theory of incompressible flows with applications to fluid dynamics, Mathematical Surveys and Monographs, 119. American Mathematical Society, Providence, RI, 2005. x+234 pp. ISBN: 0-8218-3693-5 |
[13] |
T. Ma and S. Wang, Stability and Bifurcation of Nolinear Evolution Equations, Science Press, Beijing, 2007. |
[14] |
R. V. Polovin and V. P. Demutskii, Fundamentals of Magnetohydrodynamics, Consultants Bureau, New York, 1990. |
[15] |
G. I. Taylor, Stability of a viscous liquid contained between two rotating cyinders,, Phil. Trans. Roy. Soc. Lond. A, 223 (): 289.
|
[16] |
W. Velte, Stabilit$\ddota$t and verzweigung station$\ddotarer$ l$\ddot{0}$sungen der davier-stokeschen gleichungen beim Taylorproblem, Arch. Ration. Mech. Anal., 22 (1966), 1-14.
doi: 10.1007/BF00281240. |
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