scholarly journals The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential

2012 ◽  
Vol 262 (3) ◽  
pp. 915-1010 ◽  
Author(s):  
R. Alexandre ◽  
Y. Morimoto ◽  
S. Ukai ◽  
C.-J. Xu ◽  
T. Yang
Keyword(s):  
Boltzmann Equation ◽  
Global Existence ◽  
Soft Potential ◽  
The Boltzmann Equation ◽  
Whole Space

scholarly journals THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL

2011 ◽  
Vol 09 (02) ◽  
pp. 113-134 ◽  
Author(s):  
R. ALEXANDRE ◽  
Y. MORIMOTO ◽  
S. UKAI ◽  
C.-J. XU ◽  
T. YANG
Keyword(s):  
Cauchy Problem ◽  
Boltzmann Equation ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Existence Of Solution ◽  
The Boltzmann Equation ◽  
The Cauchy Problem ◽  
Whole Space ◽  
Global Equilibrium

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces for hard potential when the solution is a small perturbation of a global equilibrium.

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