Existence of boundary layers to the Boltzmann equation with cutoff soft potentials

2007 ◽  
Vol 48 (7) ◽  
pp. 073304 ◽  
Author(s):  
Weike Wang ◽  
Tong Yang ◽  
Xiongfeng Yang
Keyword(s):  
Boltzmann Equation ◽  
Boundary Layers ◽  
The Boltzmann Equation

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

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