scholarly journals An asymptotic analysis of spherically symmetric perfect fluid self-similar solutions

2000 ◽  
Vol 17 (20) ◽  
pp. 4339-4352 ◽  
Author(s):  
B J Carr ◽  
A A Coley
Keyword(s):  
Asymptotic Analysis ◽  
Perfect Fluid ◽  
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.

scholarly journals GRAVITATIONAL COLLAPSE OF A MASSLESS SCALAR FIELD AND A PERFECT FLUID WITH SELF-SIMILARITY OF THE FIRST KIND IN 2+1 DIMENSIONS

2008 ◽  
Vol 17 (11) ◽  
pp. 2143-2158 ◽  
Author(s):  
F. I. M. PEREIRA ◽  
R. CHAN
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Self Similarity ◽  
Global Properties ◽  
Self Similar ◽  
Similar Solutions

Self-similar solutions of a collapsing perfect fluid and a massless scalar field with kinematic self-similarity of the first kind in 2+1 dimensions are obtained. The local and global properties of the solutions are studied. It is found that some of them represent gravitational collapse, in which black holes are always formed, and some may be interpreted as representing cosmological models.

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.

scholarly journals Timelike self-similar spherically symmetric perfect-fluid models

1998 ◽  
Vol 15 (9) ◽  
pp. 2841-2863 ◽  
Author(s):  
Martin Goliath ◽  
Ulf S Nilsson ◽  
Claes Uggla
Keyword(s):  
Perfect Fluid ◽  
Spherically Symmetric ◽  
Fluid Models ◽  
Perfect Fluid Models ◽  
Self Similar

scholarly journals On blow up for the energy super critical defocusing nonlinear Schrödinger equations

2021 ◽  
Author(s):  
Frank Merle ◽  
Pierre Raphaël ◽  
Igor Rodnianski ◽  
Jeremie Szeftel
Keyword(s):  
Blow Up ◽  
Companion Paper ◽  
Spherically Symmetric ◽  
Unique Strong Solution ◽  
Nonlinear Schrödinger ◽  
Degeneracy Condition ◽  
Highly Oscillatory ◽  
Self Similar ◽  
Similar Solutions ◽  
Symmetric Initial Data

AbstractWe consider the energy supercritical defocusing nonlinear Schrödinger equation $$\begin{aligned} i\partial _tu+\Delta u-u|u|^{p-1}=0 \end{aligned}$$ i ∂ t u + Δ u - u | u | p - 1 = 0 in dimension $$d\ge 5$$ d ≥ 5 . In a suitable range of energy supercritical parameters (d, p), we prove the existence of $${\mathcal {C}}^\infty $$ C ∞ well localized spherically symmetric initial data such that the corresponding unique strong solution blows up in finite time. Unlike other known blow up mechanisms, the singularity formation does not occur by concentration of a soliton or through a self similar solution, which are unknown in the defocusing case, but via a front mechanism. Blow up is achieved by compression for the associated hydrodynamical flow which in turn produces a highly oscillatory singularity. The front blow up profile is chosen among the countable family of $${\mathcal {C}}^\infty $$ C ∞ spherically symmetric self similar solutions to the compressible Euler equation whose existence and properties in a suitable range of parameters are established in the companion paper (Merle et al. in Preprint (2019)) under a non degeneracy condition which is checked numerically.

GRAVITATIONAL COLLAPSE OF A MASSLESS SCALAR FIELD AND A PERFECT FLUID WITH SELF-SIMILARITY OF THE SECOND KIND IN (2 + 1) DIMENSIONS

2006 ◽  
Vol 15 (02) ◽  
pp. 131-152 ◽  
Author(s):  
F. I. M. PEREIRA ◽  
R. CHAN ◽  
AN ZHONG WANG
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Self Similarity ◽  
Global Properties ◽  
Self Similar ◽  
Similar Solutions

Self-similar solutions of a collapsing perfect fluid and a massless scalar field with kinematic self-similarity of the second kind in (2 + 1) dimensions are obtained. The local and global properties of the solutions are studied. It is found that some of them represent gravitational collapse, in which black holes are always formed, and some may be interpreted as representing cosmological models.

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