On the Boltzmann equation part II: The full initial value problem

1972 ◽  
Vol 45 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Leif Arkeryd
Keyword(s):  
Boltzmann Equation ◽  
Initial Value Problem ◽  
Initial Value ◽  
The Boltzmann Equation

On the initial value problem for the Boltzmann equation with a force term

1989 ◽  
Vol 18 (1) ◽  
pp. 87-102 ◽  
Author(s):  
N. Bellomo ◽  
M. Lachowicz ◽  
A. Palczewski ◽  
G. Toscani
Keyword(s):  
Boltzmann Equation ◽  
Initial Value Problem ◽  
Force Term ◽  
Initial Value ◽  
The Boltzmann Equation

SOME MATHEMATICAL RESULTS ON THE ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS TO THE INITIAL VALUE PROBLEM FOR THE ENSKOG EQUATION

1989 ◽  
Vol 01 (02n03) ◽  
pp. 183-196
Author(s):  
N. BELLOMO ◽  
M. LACHOWICZ
Keyword(s):  
Boltzmann Equation ◽  
Asymptotic Behaviour ◽  
Knudsen Number ◽  
Initial Value Problem ◽  
Hydrodynamic Limit ◽  
Enskog Equation ◽  
Asymptotic Equivalence ◽  
Initial Value ◽  
The Boltzmann Equation

This paper deals with the analysis of some mathematical results on the asymptotic behaviour of the solutions to the initial value problem for the Enskog equation when the radius of the gas particles and the Knudsen number tend to zero, that is, respectively, analysis of the asymptotic equivalence with the Boltzmann equation and hydrodynamic limit.

Generalized Invariant Sets for the Boltzmann Equation

1997 ◽  
Vol 07 (04) ◽  
pp. 457-476 ◽  
Author(s):  
T. Goudon
Keyword(s):  
Boltzmann Equation ◽  
Initial Data ◽  
Global Existence ◽  
Existence Of Solutions ◽  
Invariant Set ◽  
Invariant Sets ◽  
Soft Or ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
The Boltzmann Equation

We are interested in the initial value problem for the Boltzmann equation, when the initial data u0 belongs to a set B0 = {δ0m1 (0,x,v) ≤ u0(x,v) ≤ C0m2 (0,x,v)} where m1, m2 are traveling Maxwellians. We consider soft or Maxwell's interactions with cutoff (7/3 < s ≤ 5) and C0 smaller than a bound depending on the coefficients of m2. We obtain global existence of solutions remaining in a "generalized invariant set" Bt ⊂ B∞, characterized by these particular states.

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