Self-Similar Solutions to the Spherically-Symmetric Euler Equations with a Two-Constant Equation of State

2019 ◽  
Vol 50 (1) ◽  
pp. 35-49
Author(s):  
Qitao Zhang ◽  
Yanbo Hu
Keyword(s):  
Equation Of State ◽  
Euler Equations ◽  
Spherically Symmetric ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Self-similar Langmuir collapse at critical dimension

1991 ◽  
Vol 9 (2) ◽  
pp. 363-370 ◽  
Author(s):  
L. Bergé ◽  
PH. Dousseau ◽  
G. Pelletier ◽  
D. Pesme
Keyword(s):  
Control Parameter ◽  
Linear Time ◽  
Critical Dimension ◽  
Singular Solutions ◽  
Spherically Symmetric ◽  
Scalar Model ◽  
Contraction Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Time Contraction

Two spherically symmetric versions of a self-similar collapse are investigated within the framework of the Zakharov equations, namely, one relative to a vectorial electric field and the other corresponding to a scalar modeling of the Langmuir field. Singular solutions of both of them depend on a linear time contraction rate Ξ(t) = V(t* – t), where t* and V = – Ξ denote, respectively, the collapse time and the constant collapse velocity. We show that under certain conditions, only the scalar model admits self-similar solutions, varying regularly as a function of the control parameter V from the subsonic (V ≪ 1) to the supersonic (V ≫ 1) regime.

Self-similar solutions of the Euler equations with spherical symmetry

2012 ◽  
Vol 75 (17) ◽  
pp. 6370-6378 ◽  
Author(s):  
Chen-Chang Peng ◽  
Wen-Ching Lien
Keyword(s):  
Euler Equations ◽  
Spherical Symmetry ◽  
Self Similar ◽  
Similar Solutions

scholarly journals ON THE PHYSICAL PROPERTIES OF SPHERICALLY SYMMETRIC SELF-SIMILAR SOLUTIONS

2005 ◽  
Vol 14 (01) ◽  
pp. 73-84 ◽  
Author(s):  
M. SHARIF ◽  
SEHAR AZIZ
Keyword(s):  
Physical Properties ◽  
Radial Direction ◽  
The Self ◽  
Spherically Symmetric ◽  
Self Similar ◽  
Similar Solutions ◽  
Kinematic Properties

In this paper, we are exploring some of the properties of the self-similar solutions of the first kind. In particular, we shall discuss the kinematic properties and also check the singularities of these solutions. We discuss these properties both in co-moving and also in non-co-moving (only in the radial direction) coordinates. Some interesting features of these solutions turn up.

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