scholarly journals The Vlasov–Poisson system with infinite kinetic energy and initial data in Lp(R6)

2008 ◽  
Vol 341 (1) ◽  
pp. 548-558 ◽  
Author(s):  
Xianwen Zhang ◽  
Jinbo Wei
Keyword(s):  
Kinetic Energy ◽  
Initial Data ◽  
Poisson System

THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D

1993 ◽  
Vol 03 (01) ◽  
pp. 109-124 ◽  
Author(s):  
PETER A. MARKOWICH ◽  
NORBERT J. MAUSER
Keyword(s):  
Kinetic Energy ◽  
Initial Density ◽  
Poisson System ◽  
Planck Constant ◽  
Density Matrices ◽  
Accumulation Points ◽  
Schmidt Norm ◽  
Bounded Trace ◽  
The Given ◽  
Uniformly Bounded

Under natural assumptions on the initial density matrix of a mixed quantum state (Hermitian, non-negative definite, uniformly bounded trace, Hilbert-Schmidt norm and kinetic energy) we prove that accumulation points (as the scaled Planck constant tends to zero) of solutions of a corresponding slightly regularized Wigner-Poisson system are distributional solutions of the classical Vlasov-Poisson system. The result holds for the gravitational and repulsive cases. Also, for every phase-space density in [Formula: see text] (with bounded kinetic energy) we prepare a sequence of density matrices satisfying the above assumptions, such that the given density is the limit of the Wigner transforms of these density matrices.

scholarly journals A DYNAMICAL SYMMETRY OF THE QUASI-SPHERICAL (OR SPHERICAL) COLLAPSE

2005 ◽  
Vol 14 (10) ◽  
pp. 1761-1767 ◽  
Author(s):  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY ◽  
NARESH DADHICH
Keyword(s):  
Kinetic Energy ◽  
Initial Data ◽  
Dynamical Symmetry ◽  
Matter Field ◽  
Physical Parameters ◽  
Data Sets ◽  
Type I ◽  
Data Set ◽  
Spherical Collapse ◽  
Scaling Relationship

By linearly scaling the initial data set (mass and kinetic energy functions), it is found that the dynamics of quasi-spherical (or spherical) collapse remains invariant for dust or a general (Type I) matter field, provided the comoving radius is also appropriately scaled. This defines a symmetry of the quasi spherical (or spherical) collapse. That is, the linear transformation identifies an equivalence class of data sets which lead to the same end result as well as its evolution all through. In particular, it is shown that the physical parameters, density and shear remain invariant. What the transformation is exhibiting is an interesting scaling relationship between mass, kinetic energy and the size of the collapsing sphere which is respected not only by the initial data set but remarkably also by the dynamics of collapse.

scholarly journals Convergence from two-species Vlasov-Poisson-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Poisson system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhendong Fang ◽  
Hao Wang
Keyword(s):  
Initial Data ◽  
Knudsen Number ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Poisson System ◽  
Small Initial Data ◽  
Uniform Estimates ◽  
Poisson Boltzmann ◽  
Two Fluid

<p style='text-indent:20px;'>In this paper, we obtain the uniform estimates with respect to the Knudsen number <inline-formula><tex-math id="M1">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> for the fluctuations <inline-formula><tex-math id="M2">\begin{document}$ g^{\pm}_{\varepsilon} $\end{document}</tex-math></inline-formula> to the two-species Vlasov-Poisson-Boltzmann (in briefly, VPB) system. Then, we prove the existence of the global-in-time classical solutions for two-species VPB with all <inline-formula><tex-math id="M3">\begin{document}$ \varepsilon \in (0,1] $\end{document}</tex-math></inline-formula> on the torus under small initial data and rigorously derive the convergence to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (in briefly, NSFP) system as <inline-formula><tex-math id="M4">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> go to 0.</p>

scholarly journals Asymptotic limit of nonlinear Schrödinger-Poisson system with general initial data

2011 ◽  
Vol 4 (3) ◽  
pp. 767-783
Author(s):  
Qiangchang Ju ◽  
◽  
Fucai Li ◽  
Hailiang Li ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Asymptotic Limit ◽  
Poisson System ◽  
Nonlinear Schrödinger ◽  
General Initial Data
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