Pulsating flows of the 2D Euler–Poisson equations
Tài liệu tham khảo
Bezard, 1993, Existence locale de solutions pour les equations d'Euler–Poisson, Jpn. J. Ind. Appl. Math., 10, 431, 10.1007/BF03167283
Binney, 1994
Chae, 2008, On the finite time blow-up of the Euler–Poisson equations in RN, Commun. Math. Sci., 6, 785, 10.4310/CMS.2008.v6.n3.a13
Chandrasekhar, 1939
Corless, 1996, On the Lambert W function, Adv. Comput. Math., 5, 329, 10.1007/BF02124750
Deng, 2002, Solutions of Euler–Poisson equations for gaseous stars, Arch. Ration. Mech. Anal., 164, 261, 10.1007/s00205-002-0209-6
Deng, 2003, Blowup phenomena of solutions to Euler–Poisson equations, J. Math. Anal. Appl., 286, 295, 10.1016/S0022-247X(03)00487-6
Engelberg, 2001, Critical thresholds in Euler–Poisson equations, Indiana Univ. Math. J., 50, 109, 10.1512/iumj.2001.50.2177
Engelberg, 1996, Formation of singularities in the Euler and Euler–Poisson equations, Phys. D, 98, 67, 10.1016/0167-2789(96)00087-5
Fliche, 2007, Euler–Poisson–Newton approach in cosmology, vol. 910, 346
Gamblin, 1993, Solution reguliere a temps petit pour l'equation d'Euler–Poisson, Comm. Partial Differential Equations, 18, 731, 10.1080/03605309308820948
Glassey, 1996
Goldreich, 1980, Homologously collapsing stellar cores, Astrophys. J., 238, 991, 10.1086/158065
Jang, 2008, Nonlinear instability in gravitational Euler–Poisson systems for γ=6/5, Arch. Ration. Mech. Anal., 188, 265, 10.1007/s00205-007-0086-0
Li, 1991, On uniformly rotating stars, Arch. Ration. Mech. Anal., 115, 367, 10.1007/BF00375280
Lin, 1997, Stability of gaseous stars in spherically symmetric motions, SIAM J. Math. Anal., 28, 539, 10.1137/S0036141095292883
Liu, 2004, Rotation prevents finite-time breakdown, Phys. D, 188, 262, 10.1016/j.physd.2003.07.006
Liu, 2003, Critical thresholds in 2D restricted Euler–Poisson equations, SIAM J. Appl. Math., 63, 1889, 10.1137/S0036139902416986
Luo, 2004, Rotating fluids with self-gravitation in bounded domains, Arch. Ration. Mech. Anal., 173, 345, 10.1007/s00205-004-0319-4
Makino, 1986, On a local existence theorem for the evolution equation of gaseous stars, vol. 18, 459
Makino, 1990, Sur les Solutions a symmetric spherique de lequation d'Euler–Poisson Pour levolution d'etoiles gazeuses, Jpn. J. Ind. Appl. Math., 7, 165, 10.1007/BF03167897
Neukirch, 2001, A class of accelerated solutions of the two-dimensional ideal magnetodynamic equations, Proc. R. Soc. Lond. A, 457, 2547, 10.1098/rspa.2001.0842
Tassoul, 1978
Yuen, 2008, Analytical blowup solutions to the 2-dimensional isothermal Euler–Poisson equations of gaseous stars, J. Math. Anal. Appl., 341, 445, 10.1016/j.jmaa.2007.10.026
Yuen, 2008, Stabilities for Euler–Poisson equations in some special dimensions, J. Math. Anal. Appl., 344, 145, 10.1016/j.jmaa.2008.02.025
Yuen, 2011, Analytical blowup solutions to the 2-dimensional isothermal Euler–Poisson equations of gaseous stars II, J. Math. Phys., 52, 10.1063/1.3614504
Yuen, 2011, Blowup for the C1 solutions of the Euler–Poisson equations of gaseous stars in RN, J. Math. Anal. Appl., 383, 627, 10.1016/j.jmaa.2011.05.048
Kwong, 2014, Periodic solutions of 2D isothermal Euler–Poisson equations with possible applications to spiral and disk-like galaxies, J. Math. Anal. Appl., 420, 1854, 10.1016/j.jmaa.2014.06.033