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Euler-Poisson equations related to general compressible rotating fluids
1. | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China, China |
References:
[1] |
J. F. G. Auchmuty, Existence of equilibrium figures, Arch. Rational Mech. Anal., 65 (1977), 249-261.
doi: 10.1007/BF00280443. |
[2] |
J. F. G. Auchmuty, The global branching of rotating stars, Arch. Rational Mech. Anal., 114 (1991), 179-194.
doi: 10.1007/BF00375402. |
[3] |
J. F. G. Auchmuty and R. Beals, Variation solutions of some non-linear free boundary problems, Arch. Rational Mech. Anal., 43 (1971), 255-271.
doi: 10.1007/BF00250465. |
[4] |
J. F. G. Auchmuty and R. Beals, Models of rotating stars, Astrophysical J., 165 (1971), 79-82.
doi: 10.1086/180721. |
[5] |
L. A. Caffarelli and A. Friedman, The shape of axisymmetric rotating fluid, J. Funct. Anal., 35 (1980), 109-142.
doi: 10.1016/0022-1236(80)90082-8. |
[6] |
S. Chandrasekhar, "Introduction to the Stellar Structure," University of Chicago Press, 1939 |
[7] |
S. Chandrasekhar, "Ellipsoidal Figures of Equilibrium," Dover Publication Inc., New York, 1987 |
[8] |
S. Chanillo and Y. Y. Li, On diameters of uniformly rotating stars, Comm. Math. Phys., 166 (1994), 417-430.
doi: 10.1007/BF02112323. |
[9] |
A. Friedman and B. Turkington, Asymptotic estimates for an axisymmetric rotating fluid, J. Fun. Anal., 37 (1980), 136-163.
doi: 10.1016/0022-1236(80)90038-5. |
[10] |
A. Friedman and B. Turkington, The oblateness of an axisymmetric rotating fluid, Indiana Univ. Math. J., 29 (1980), 777-792.
doi: 10.1512/iumj.1980.29.29056. |
[11] |
A. Friedman and B. Turkington, Existence and dimensions of a rotating white dwarf, J. Diff. Equations, 42 (1981), 414-437.
doi: 10.1016/0022-0396(81)90114-5. |
[12] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," 2nd edition, Springer, 1983. |
[13] |
G. H. Hardy, J. E. Littlewood and G. Polya, "Inequality," Cambridge Univ. Press, Cambridge, 1934. |
[14] |
J. Jang, Nonlinear instability in gravitational Euler-Poisson system for $\gamma=\frac{6}{5}$, Arch. Rational Mech. Anal., 188 (2008), 265-307.
doi: 10.1007/s00205-007-0086-0. |
[15] |
H. G. Li and J. G. Bao, Existence of the rotating stars with prescribed angular velocity law, to appear in Houston J. Math. |
[16] |
Y. Y. Li, On uniformly rotating stars, Arch. Rational Mech. Anal., 115 (1991), 367-393.
doi: 10.1007/BF00375280. |
[17] |
P. L. Lions, The concentration-compactness principle in the calculus of variation, The locally case, part I, Ann. I. H. Anal. Nonli., 1 (1984), 109-145. |
[18] |
P. L. Lions, Minimization problems in $L^1(\bb R^3)$, J. Funct. Anal., 41 (1981), 236-275.
doi: 10.1016/0022-1236(81)90089-6. |
[19] |
T. Luo and J. Smoller, Rotating fluids with self-gravitation in bounded domains, Arch. Rational Mech. Anal., 173 (2004), 345-377. |
[20] |
T. Luo and J. Smoller, Nonlinear dynamical stability of Newtonian rotating white dwarfs and supermassive stars, Comm. Math. Physics, 284 (2008), 425-457.
doi: 10.1007/s00220-008-0569-3. |
[21] |
T. Luo and J. Smoller, Existence and nonlinear stability of rotating star solutions of the compressible Euler-Poisson equations, Arch. Rational Mech. Anal., 191 (2009), 447-496.
doi: 10.1007/s00205-007-0108-y. |
[22] |
R. J. McCann, Stable rotating binary stars and fluid in a tube, Houston J. Math., 32 (2006), 603-632. |
[23] |
G. Rein, Reduction and a concentration-compactness principle for energy-Casimir functionals, SIAM J. Math. Anal., 33 (2001), 896-912.
doi: 10.1137/P0036141001389275. |
[24] |
S. H. Shapiro and S. A. Teukolsky, "Black Holes, White Dwarfs, and Neutron Stars," WILEY-VCH, New York, 1983.
doi: 10.1002/9783527617661. |
[25] |
J. L. Tassoul, "Theory of Rotating Stars," Princeton Univ. Press, New Jersey, 1978. |
[26] |
S. Weinberg, "Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity," John Wiley and Sons, Inc. New York, 1972. |
show all references
References:
[1] |
J. F. G. Auchmuty, Existence of equilibrium figures, Arch. Rational Mech. Anal., 65 (1977), 249-261.
doi: 10.1007/BF00280443. |
[2] |
J. F. G. Auchmuty, The global branching of rotating stars, Arch. Rational Mech. Anal., 114 (1991), 179-194.
doi: 10.1007/BF00375402. |
[3] |
J. F. G. Auchmuty and R. Beals, Variation solutions of some non-linear free boundary problems, Arch. Rational Mech. Anal., 43 (1971), 255-271.
doi: 10.1007/BF00250465. |
[4] |
J. F. G. Auchmuty and R. Beals, Models of rotating stars, Astrophysical J., 165 (1971), 79-82.
doi: 10.1086/180721. |
[5] |
L. A. Caffarelli and A. Friedman, The shape of axisymmetric rotating fluid, J. Funct. Anal., 35 (1980), 109-142.
doi: 10.1016/0022-1236(80)90082-8. |
[6] |
S. Chandrasekhar, "Introduction to the Stellar Structure," University of Chicago Press, 1939 |
[7] |
S. Chandrasekhar, "Ellipsoidal Figures of Equilibrium," Dover Publication Inc., New York, 1987 |
[8] |
S. Chanillo and Y. Y. Li, On diameters of uniformly rotating stars, Comm. Math. Phys., 166 (1994), 417-430.
doi: 10.1007/BF02112323. |
[9] |
A. Friedman and B. Turkington, Asymptotic estimates for an axisymmetric rotating fluid, J. Fun. Anal., 37 (1980), 136-163.
doi: 10.1016/0022-1236(80)90038-5. |
[10] |
A. Friedman and B. Turkington, The oblateness of an axisymmetric rotating fluid, Indiana Univ. Math. J., 29 (1980), 777-792.
doi: 10.1512/iumj.1980.29.29056. |
[11] |
A. Friedman and B. Turkington, Existence and dimensions of a rotating white dwarf, J. Diff. Equations, 42 (1981), 414-437.
doi: 10.1016/0022-0396(81)90114-5. |
[12] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," 2nd edition, Springer, 1983. |
[13] |
G. H. Hardy, J. E. Littlewood and G. Polya, "Inequality," Cambridge Univ. Press, Cambridge, 1934. |
[14] |
J. Jang, Nonlinear instability in gravitational Euler-Poisson system for $\gamma=\frac{6}{5}$, Arch. Rational Mech. Anal., 188 (2008), 265-307.
doi: 10.1007/s00205-007-0086-0. |
[15] |
H. G. Li and J. G. Bao, Existence of the rotating stars with prescribed angular velocity law, to appear in Houston J. Math. |
[16] |
Y. Y. Li, On uniformly rotating stars, Arch. Rational Mech. Anal., 115 (1991), 367-393.
doi: 10.1007/BF00375280. |
[17] |
P. L. Lions, The concentration-compactness principle in the calculus of variation, The locally case, part I, Ann. I. H. Anal. Nonli., 1 (1984), 109-145. |
[18] |
P. L. Lions, Minimization problems in $L^1(\bb R^3)$, J. Funct. Anal., 41 (1981), 236-275.
doi: 10.1016/0022-1236(81)90089-6. |
[19] |
T. Luo and J. Smoller, Rotating fluids with self-gravitation in bounded domains, Arch. Rational Mech. Anal., 173 (2004), 345-377. |
[20] |
T. Luo and J. Smoller, Nonlinear dynamical stability of Newtonian rotating white dwarfs and supermassive stars, Comm. Math. Physics, 284 (2008), 425-457.
doi: 10.1007/s00220-008-0569-3. |
[21] |
T. Luo and J. Smoller, Existence and nonlinear stability of rotating star solutions of the compressible Euler-Poisson equations, Arch. Rational Mech. Anal., 191 (2009), 447-496.
doi: 10.1007/s00205-007-0108-y. |
[22] |
R. J. McCann, Stable rotating binary stars and fluid in a tube, Houston J. Math., 32 (2006), 603-632. |
[23] |
G. Rein, Reduction and a concentration-compactness principle for energy-Casimir functionals, SIAM J. Math. Anal., 33 (2001), 896-912.
doi: 10.1137/P0036141001389275. |
[24] |
S. H. Shapiro and S. A. Teukolsky, "Black Holes, White Dwarfs, and Neutron Stars," WILEY-VCH, New York, 1983.
doi: 10.1002/9783527617661. |
[25] |
J. L. Tassoul, "Theory of Rotating Stars," Princeton Univ. Press, New Jersey, 1978. |
[26] |
S. Weinberg, "Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity," John Wiley and Sons, Inc. New York, 1972. |
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