On the Cauchy Problem of an Extended Nonlinear Bose-Einstein Equation with Critical Nonlinear Damping in R3

2021 ◽  
pp. 215-230
Author(s):  
Brahim Alouini
Keyword(s):  
Cauchy Problem ◽  
Einstein Equation ◽  
Nonlinear Damping ◽  
The Cauchy Problem ◽  
Bose Einstein

scholarly journals Relativistic BGK model for massless particles in the FLRW spacetime

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Byung-Hoon Hwang ◽  
Ho Lee ◽  
Seok-Bae Yun
Keyword(s):  
Cauchy Problem ◽  
Particle Number ◽  
Sufficient Conditions ◽  
Initial Step ◽  
Explicit Solutions ◽  
Bgk Model ◽  
Massless Particles ◽  
Existence Of Equilibrium ◽  
The Cauchy Problem ◽  
Bose Einstein

<p style='text-indent:20px;'>In this paper, we address the Cauchy problem for the relativistic BGK model proposed by Anderson and Witting for massless particles in the Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime. We first derive the explicit form of the Jüttner distribution in the FLRW spacetime, together with a set of nonlinear relations that leads to the conservation laws of particle number, momentum, and energy for both Maxwell-Boltzmann particles and Bose-Einstein particles. Then, we find sufficient conditions that guarantee the existence of equilibrium coefficients satisfying the nonlinear relations and we show that the condition is satisfied through all the induction steps once it is verified for the initial step. Using this observation, we construct explicit solutions of the relativistic BGK model of Anderson-Witting type for massless particles in the FLRW spacetime.</p>

On the cauchy problem for the einstein equation

2012 ◽  
Vol 86 (3) ◽  
pp. 781-783 ◽  
Author(s):  
V. V. Lychagin ◽  
V. A. Yumaguzhin
Keyword(s):  
Cauchy Problem ◽  
Einstein Equation ◽  
The Cauchy Problem

On the spin-1 Bose–Einstein condensates in the presence of Ioffe–Pritchard magnetic field

2016 ◽  
Vol 18 (05) ◽  
pp. 1550062
Author(s):  
Hichem Hajaiej ◽  
Rémi Carles
Keyword(s):  
Magnetic Field ◽  
Cauchy Problem ◽  
Ground State ◽  
Standing Waves ◽  
Einstein Condensate ◽  
Ground State Solutions ◽  
Bose Einstein Condensate ◽  
The Cauchy Problem ◽  
Bose Einstein ◽  
Antiferromagnetic Spin

We study the Cauchy problem of an antiferromagnetic spin-1 Bose–Einstein condensate under Ioffe–Pritchard magnetic field [Formula: see text]. We then address the existence of ground state solutions and characterize the orbit of standing waves.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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