Green's Function and Pointwise Space-time Behaviors of the Three-Dimensional Relativistic Boltzmann Equation

2024/05/10 by Yanchao Li, Li, Yanchao, Mingying Zhong +1
Mathematics · Engineering · #Gas Dynamics and Kinetic Theory #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2405.06280

Abstract

The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed √(a²+b²) at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear relativistic Boltzmann equation with non-smooth initial data based on the Green's function.

Related

• Green's function and Pointwise Behavior of the One-Dimensional Vlasov-Maxwell-Boltzmann System
• Green's Function and Pointwise Behaviors of the Vlasov-Poisson-Fokker-Planck System
• Global existence of solutions for the relativistic Boltzmann equation on the flat Robertson-Walker space-time for arbitrarily large intial data
• Spectrum analysis for the relativistic Boltzmann equation
• Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation