scholarly journals On Smooth Solutions to the Thermostated Boltzmann Equation with Deformation

2022 ◽  
Vol 1 (1) ◽  
pp. 152-212
Author(s):  
Renjun Duan & Shuangqian Liu
Keyword(s):  
Boltzmann Equation ◽  
Smooth Solutions

LOCAL SMOOTH SOLUTIONS OF A THIN SPRAY MODEL WITH COLLISIONS

2010 ◽  
Vol 20 (02) ◽  
pp. 191-221 ◽  
Author(s):  
JULIEN MATHIAUD
Keyword(s):  
Boltzmann Equation ◽  
Initial Data ◽  
Euler Equations ◽  
Existence And Uniqueness ◽  
Well Posedness ◽  
Liquid Droplets ◽  
Smooth Solutions ◽  
Perfect Gas ◽  
Complex Flows

Sprays are complex flows made of liquid droplets surrounded by a gas. The aim of this paper is to study the local in time well-posedness of a collisional thin spray model, that is a coupling between Euler equations for a perfect gas and a Vlasov–Boltzmann equation for the droplets. We prove the existence and uniqueness of (local in time) solutions for this problem as soon as initial data are smooth enough.

The imprint of GWs on the CMB

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Boltzmann Equation ◽  
Cmb Polarization

CMB multipoles. Photon geodesics in perturbed FRW. Temperature anisotropies. Sachs-Wolfe, ISW and Doppler contributions. Boltzmann equation. CMB polarization. E and B modes

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

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.

Sign in / Sign up

Export Citation Format

Share Document