Almost Exponential Decay Near Maxwellian

ABSTRACT

By direct interpolation of a family of smooth energy estimates for solutions near Maxwellian equilibrium and in a periodic box to several Boltzmann type equations in Guo (2002 2003a b) and Strain and Guo (2004), we show convergence to Maxwellian with any polynomial rate in time. Our results not only resolve the important open problem for both the Vlasov-Maxwell-Boltzmann system and the relativistic Landau-Maxwell system for charged particles, but also lead to a simpler alternative proof of recent decay results (Desvillettes and Villani, 2005) for soft potentials as well as the Coulombic interaction, with precise decay rate depending on the initial conditions.

Keywords:

• Boltzmann
• Landau
• Maxwell
• Vlasov-Maxwell-Boltzmann system
• Collisional kinetic theory
• Convergence to Maxwellian
• Energy method
• Relativistic Landau-Maxwell system

Mathematics Subject Classification:

• 82B40
• 82C40
• 82D05
• 82D10