Inflow boundary value problems of the stationary relativistic Boltzmann equation

报告题目： Inflow boundary value problems of the stationary relativistic Boltzmann equation

报 告 人： 李莉 教授， 宁波大学

时    间： 2025年06月29日（星期日）10:00-11:00

地    点： 思源楼615

摘    要： We study the inflow boundary value problem of steady-state relativistic Boltzmann equation 

in half-line with hard potential model, given the data for the incoming particles at the boundary and 

a relativistic global Maxwellian with nonzero macroscopic velocities at the far field. We first explicitly 

address the sound speed for the relativistic Maxwellian in the far field, according to the eigenvalues 

of a finite dimensional operator based on macroscopic projection. Then we demonstrate that the 

solvability of the problem varies with the Mach number. The proof is based on the macro-micro 

decomposition of solutions combined with an artificial damping term. Singular in velocity and 

spatially exponential decay weights are chosen to carry out the energy estimates. The result extends 

the previous work (Ukai, Yang and Yu, 2003, Commun. Math. Phys.) to the relativistic problem.