Using modern mathematical techniques from the fields of partial differential equations and harmonic analysis - many of which were developed during the last five to 50 years, and thus relatively new to mathematics - the mathematicians proved the global existence of classical solutions and rapid time decay to equilibrium for the Boltzmann equation
with long-range interactions.
Unfortunately, solving the linear Boltzmann equation
is difficult: standard numerical schemes can be inaccurate and computationally inefficient.
The proposed work on the Boltzmann equation
is a continuation of previous works of the applicant in collaboration with M.
After obtaining the stochastic Kac dynamics in the momentum space from the stochastic dynamics in the phase space, he shows that the spatially homogenous Boltzmann equation
can be derived from the stochastic Boltzmann hierarchy in the phase space without using mean-field approximation.
Starting from the Boltzmann equation
, Guyer and Krumhansl (1966) derived an equation of the form (3.
Thirring (eds), The Boltzmann Equation
, Wien, Springer-Verlag, pp.
The speakers examine Brownian motion in a wedge, the semiclassical focusing nonlinear Schrodinger equation, the dynamics of turbulent flows near smooth walls, the incompressible Navier-Stokes limit of the Boltzmann equation
, and hyperbolic conservation laws with involutions and contingent entropies.
The kinetic theory based on the Boltzmann equation
accurately describes the microscopic interaction properties, and has been widely used in the simulation of particle-liquid two-phase flows.
In the classical physics problem, the behavior of gases, the interaction potential is known; it can be derived from the Boltzmann equation
It has, however, been revised to include more extensive reference to applications of material covered and the addition of appendices on applied mathematics topics, the Boltzmann equation
, and a summary of the basic equations in several coordinate systems.
Here, we make use of an interpolation formula based on the numerical solution of Boltzmann equation
for the ratio of the evaporation rate in the slip and transition regime ([10.