4 research outputs found
The Global Well-Posedness of the Relativistic Boltzmann Equation with Diffuse Reflection Boundary Condition in Bounded Domains
The relativistic Boltzmann equation in bounded domains has been widely used
in physics and engineering, for example, Tokamak devices in fusion reactors.In
spite of its importance, there has, to the best of our knowledge, been no
mathematical theory on the global existence of solutions to the relativistic
Boltzmann equation in bounded domains. In the present paper, assuming that the
motion of single-species relativistic particles in a bounded domain is governed
by the relativistic Boltzmann equation with diffuse reflection boundary
conditions of non-isothermal wall temperature of small variations around a
positive constant, and regarding the speed of light as a large
parameter, we first construct a unique non-negative stationary solution
, and further establish the dynamical stability of such stationary
solution with exponential time decay rate. We point out that the
-bound of perturbations for both steady and non-steady solutions
are independent of the speed of light , and such uniform in
estimates will be useful in the study of Newtonian limit in the
future.Comment: 61 pages. Comments are welcom
The global well-posedness and Newtonian limit for the relativistic Boltzmann equation in a periodic box
In this paper, we study the Newtonian limit for relativistic Boltzmann
equation in a periodic box . We first establish the
global-in-time mild solutions of relativistic Boltzmann equation with
uniform-in- estimates and time decay rate. Then we rigorously
justify the global-in-time Newtonian limits from the relativistic Boltzmann
solutions to the solution of Newtonian Boltzmann equation in
. Moreover, if the initial data of Newtonian Boltzmann
equation belong to , based on a
decomposition and argument, the global-in-time Newtonian limit
is proved in . The convergence rates of Newtonian limit are
obtained both in and .Comment: 56 pages, All comments are welcom