TY - JOUR
T1 - Multiplicity of stationary solutions to the Euler-Poisson equations
AU - Deng, Yinbin
AU - Yang, Tong
PY - 2006/12/1
Y1 - 2006/12/1
N2 - Consider the system of Euler-Poisson as a model for the time evolution of gaseous stars through the self-induced gravitational force. We study the existence, uniqueness and multiplicity of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy a priori. These results generalize the previous works on the irrotational or the rotational gaseous stars around an axis, and then they hold in more general physical settings. Under the assumption of radial symmetry, the monotonicity properties of the radius of the gas with respect to either the strength of the velocity field or the center density are also given which yield the uniqueness under some circumstances. © 2006 Elsevier Inc. All rights reserved.
AB - Consider the system of Euler-Poisson as a model for the time evolution of gaseous stars through the self-induced gravitational force. We study the existence, uniqueness and multiplicity of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy a priori. These results generalize the previous works on the irrotational or the rotational gaseous stars around an axis, and then they hold in more general physical settings. Under the assumption of radial symmetry, the monotonicity properties of the radius of the gas with respect to either the strength of the velocity field or the center density are also given which yield the uniqueness under some circumstances. © 2006 Elsevier Inc. All rights reserved.
KW - Compact support
KW - Euler-Poisson equations
KW - Multiple solutions
KW - Uniqueness
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-33748763562&origin=recordpage
U2 - 10.1016/j.jde.2006.05.003
DO - 10.1016/j.jde.2006.05.003
M3 - RGC 21 - Publication in refereed journal
VL - 231
SP - 252
EP - 289
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -