Global existence in L1 for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation

1990 ◽  
Vol 59 (3-4) ◽  
pp. 845-867 ◽  
Author(s):  
Leif Arkeryd ◽  
Carlo Cercignani
Keyword(s):  
Boltzmann Equation ◽  
Global Existence ◽  
Enskog Equation ◽  
The Boltzmann Equation

scholarly journals Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff

2011 ◽  
Vol 304 (2) ◽  
pp. 513-581 ◽  
Author(s):  
R. Alexandre ◽  
Y. Morimoto ◽  
S. Ukai ◽  
C. -J. Xu ◽  
T. Yang
Keyword(s):  
Boltzmann Equation ◽  
Global Existence ◽  
The Boltzmann Equation ◽  
Full Regularity

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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