Continua of steadily rotating stars
Author:
Walter A. Strauss
Journal:
Quart. Appl. Math. 81 (2023), 413-427
MSC (2020):
Primary 35Q85, 35R35, 85A15, 35Q35
DOI:
https://doi.org/10.1090/qam/1641
Published electronically:
December 29, 2022
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Additional Information
Abstract: This article is a brief survey of mathematical work, joint with Yilun Wu and Juhi Jang, on models of stars and galaxies. It is a sequel to the survey article by Yilun Wu [Quart. Appl. Math. 78 (2020), pp. 147–159]. The models consider rotating stars (or galaxies or gaseous planets) as composed of particles subject to gravity. Under appropriate conditions, global families of isentropic steadily rotating stars are shown to exist. Local families are also shown to exist even in the presence of variable entropy and arbitrary axisymmetric angular velocity.
References
- Giles Auchmuty, The global branching of rotating stars, Arch. Rational Mech. Anal. 114 (1991), no. 2, 179–193. MR 1094435, DOI 10.1007/BF00375402
- J. F. G. Auchmuty and Richard Beals, Variational solutions of some nonlinear free boundary problems, Arch. Rational Mech. Anal. 43 (1971), 255–271. MR 337260, DOI 10.1007/BF00250465
- Luis A. Caffarelli and Avner Friedman, The shape of axisymmetric rotating fluid, J. Functional Analysis 35 (1980), no. 1, 109–142. MR 560219, DOI 10.1016/0022-1236(80)90082-8
- S. Chandrasekhar, Ellipsoidal figures of equilibrium—an historical account, Comm. Pure Appl. Math. 20 (1967), 251–265. MR 213075, DOI 10.1002/cpa.3160200203
- R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, N. Y., 1948. MR 0029615
- Avner Friedman and Bruce Turkington, Existence and dimensions of a rotating white dwarf, J. Differential Equations 42 (1981), no. 3, 414–437. MR 639231, DOI 10.1016/0022-0396(81)90114-5
- U. Heilig, On Lichtenstein’s analysis of rotating Newtonian stars, Ann. Inst. H. Poincaré Phys. Théor. 60 (1994), no. 4, 457–487 (English, with English and French summaries). MR 1288588
- Juhi Jang and Tetu Makino, On slowly rotating axisymmetric solutions of the Euler-Poisson equations, Arch. Ration. Mech. Anal. 225 (2017), no. 2, 873–900. MR 3665672, DOI 10.1007/s00205-017-1115-2
- Juhi Jang and Tetu Makino, On rotating axisymmetric solutions of the Euler-Poisson equations, J. Differential Equations 266 (2019), no. 7, 3942–3972. MR 3912707, DOI 10.1016/j.jde.2018.09.023
- Juhi Jang, Walter A. Strauss, and Yilun Wu, Existence of rotating magnetic stars, Phys. D 397 (2019), 65–74. MR 3987336, DOI 10.1016/j.physd.2019.03.005
- J. Jang, W. Strauss, and Y. Wu, Existence of rotating stars with variable entropy, arXiv:2111.04634, 2021.
- Hansjörg Kielhöfer, Bifurcation theory, Applied Mathematical Sciences, vol. 156, Springer-Verlag, New York, 2004. An introduction with applications to PDEs. MR 2004250, DOI 10.1007/b97365
- Yan Yan Li, On uniformly rotating stars, Arch. Rational Mech. Anal. 115 (1991), no. 4, 367–393. MR 1120853, DOI 10.1007/BF00375280
- Leon Lichtenstein, Untersuchungen über die Gleichgewichtsfiguren rotierender Flüssigkeiten, deren Teilchen einander nach dem Newtonschen Gesetze anziehen, Math. Z. 36 (1933), no. 1, 481–562 (German). MR 1545356, DOI 10.1007/BF01188634
- Tao Luo and Joel Smoller, Existence and non-linear stability of rotating star solutions of the compressible Euler-Poisson equations, Arch. Ration. Mech. Anal. 191 (2009), no. 3, 447–496. MR 2481067, DOI 10.1007/s00205-007-0108-y
- Gerhard Rein, Stationary and static stellar dynamic models with axial symmetry, Nonlinear Anal. 41 (2000), no. 3-4, Ser. A: Theory Methods, 313–344. MR 1762148, DOI 10.1016/S0362-546X(98)00280-6
- Walter A. Strauss and Yilun Wu, Steady states of rotating stars and galaxies, SIAM J. Math. Anal. 49 (2017), no. 6, 4865–4914. MR 3732945, DOI 10.1137/17M1119391
- Walter A. Strauss and Yilun Wu, Rapidly rotating stars, Comm. Math. Phys. 368 (2019), no. 2, 701–721. MR 3949722, DOI 10.1007/s00220-019-03414-7
- Walter A. Strauss and Yilun Wu, Rapidly rotating white dwarfs, Nonlinearity 33 (2020), no. 9, 4783–4798. MR 4135095, DOI 10.1088/1361-6544/ab8d13
- W. Strauss and Y. Wu, Global continuation of a Vlasov model of rotating galaxies, arXiv:2203.01454, 2022.
- Jean-Louis Tassoul, Stellar rotation, Cambridge Astrophysics Series, vol. 36, Cambridge University Press, Cambridge, 2000. MR 1920366, DOI 10.1017/CBO9780511546044
- Yilun Wu, On rotating star solutions to the non-isentropic Euler-Poisson equations, J. Differential Equations 259 (2015), no. 12, 7161–7198. MR 3401594, DOI 10.1016/j.jde.2015.08.016
- Yilun Wu, Global continuation and the theory of rotating stars, Quart. Appl. Math. 78 (2020), no. 1, 147–159. MR 4042222, DOI 10.1090/qam/1550
References
- Giles Auchmuty, The global branching of rotating stars, Arch. Rational Mech. Anal. 114 (1991), no. 2, 179–193. MR 1094435, DOI 10.1007/BF00375402
- J. F. G. Auchmuty and Richard Beals, Variational solutions of some nonlinear free boundary problems, Arch. Rational Mech. Anal. 43 (1971), 255–271. MR 337260, DOI 10.1007/BF00250465
- Luis A. Caffarelli and Avner Friedman, The shape of axisymmetric rotating fluid, J. Functional Analysis 35 (1980), no. 1, 109–142. MR 560219, DOI 10.1016/0022-1236(80)90082-8
- S. Chandrasekhar, Ellipsoidal figures of equilibrium—an historical account, Comm. Pure Appl. Math. 20 (1967), 251–265. MR 213075, DOI 10.1002/cpa.3160200203
- R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, N. Y., 1948. MR 0029615
- Avner Friedman and Bruce Turkington, Existence and dimensions of a rotating white dwarf, J. Differential Equations 42 (1981), no. 3, 414–437. MR 639231, DOI 10.1016/0022-0396(81)90114-5
- U. Heilig, On Lichtenstein’s analysis of rotating Newtonian stars, Ann. Inst. H. Poincaré Phys. Théor. 60 (1994), no. 4, 457–487 (English, with English and French summaries). MR 1288588
- Juhi Jang and Tetu Makino, On slowly rotating axisymmetric solutions of the Euler-Poisson equations, Arch. Ration. Mech. Anal. 225 (2017), no. 2, 873–900. MR 3665672, DOI 10.1007/s00205-017-1115-2
- Juhi Jang and Tetu Makino, On rotating axisymmetric solutions of the Euler-Poisson equations, J. Differential Equations 266 (2019), no. 7, 3942–3972. MR 3912707, DOI 10.1016/j.jde.2018.09.023
- Juhi Jang, Walter A. Strauss, and Yilun Wu, Existence of rotating magnetic stars, Phys. D 397 (2019), 65–74. MR 3987336, DOI 10.1016/j.physd.2019.03.005
- J. Jang, W. Strauss, and Y. Wu, Existence of rotating stars with variable entropy, arXiv:2111.04634, 2021.
- Hansjörg Kielhöfer, Bifurcation theory, Applied Mathematical Sciences, vol. 156, Springer-Verlag, New York, 2004. An introduction with applications to PDEs. MR 2004250, DOI 10.1007/b97365
- Yan Yan Li, On uniformly rotating stars, Arch. Rational Mech. Anal. 115 (1991), no. 4, 367–393. MR 1120853, DOI 10.1007/BF00375280
- Leon Lichtenstein, Untersuchungen über die Gleichgewichtsfiguren rotierender Flüssigkeiten, deren Teilchen einander nach dem Newtonschen Gesetze anziehen, Math. Z. 36 (1933), no. 1, 481–562 (German). MR 1545356, DOI 10.1007/BF01188634
- Tao Luo and Joel Smoller, Existence and non-linear stability of rotating star solutions of the compressible Euler-Poisson equations, Arch. Ration. Mech. Anal. 191 (2009), no. 3, 447–496. MR 2481067, DOI 10.1007/s00205-007-0108-y
- Gerhard Rein, Stationary and static stellar dynamic models with axial symmetry, Nonlinear Anal. 41 (2000), no. 3-4, Ser. A: Theory Methods, 313–344. MR 1762148, DOI 10.1016/S0362-546X(98)00280-6
- Walter A. Strauss and Yilun Wu, Steady states of rotating stars and galaxies, SIAM J. Math. Anal. 49 (2017), no. 6, 4865–4914. MR 3732945, DOI 10.1137/17M1119391
- Walter A. Strauss and Yilun Wu, Rapidly rotating stars, Comm. Math. Phys. 368 (2019), no. 2, 701–721. MR 3949722, DOI 10.1007/s00220-019-03414-7
- Walter A. Strauss and Yilun Wu, Rapidly rotating white dwarfs, Nonlinearity 33 (2020), no. 9, 4783–4798. MR 4135095, DOI 10.1088/1361-6544/ab8d13
- W. Strauss and Y. Wu, Global continuation of a Vlasov model of rotating galaxies, arXiv:2203.01454, 2022.
- Jean-Louis Tassoul, Stellar rotation, Cambridge Astrophysics Series, vol. 36, Cambridge University Press, Cambridge, 2000. MR 1920366, DOI 10.1017/CBO9780511546044
- Yilun Wu, On rotating star solutions to the non-isentropic Euler-Poisson equations, J. Differential Equations 259 (2015), no. 12, 7161–7198. MR 3401594, DOI 10.1016/j.jde.2015.08.016
- Yilun Wu, Global continuation and the theory of rotating stars, Quart. Appl. Math. 78 (2020), no. 1, 147–159. MR 4042222, DOI 10.1090/qam/1550
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Additional Information
Walter A. Strauss
Affiliation:
Department of Mathematics, Brown University, Providence, RI 02912
MR Author ID:
168085
Email:
wstrauss@math.brown.edu
Received by editor(s):
August 13, 2022
Received by editor(s) in revised form:
November 9, 2022
Published electronically:
December 29, 2022
Dedicated:
Dedicated in admiration to my best friend and colleague, Costas Dafermos
Article copyright:
© Copyright 2022
Brown University