Convergence from the Two-Species Vlasov-Poisson-Boltzmann System to the Two-Fluid Incompressible Navier-Stokes-Fourier-Poisson System with Ohm's Law

作者：Fang, Zhendong^*; Jiang, Ning

来源：Acta Mathematica Scientia, 2023, 43(2): 777-820.

DOI：10.1007/s10473-023-0217-1

• two-species Vlasov-Poisson-Boltzmann system
• global-in-time classical solutions
• incompressible Navier-Stokes-Fourier-Poisson system
• Ohm's law
• uniform energy estimates
• convergence

In this paper, we justify the convergence from the two-species Vlasov-Poisson-Boltzmann (VPB, for short) system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (NSFP, for short) system with Ohm's law in the context of classical solutions. We prove the uniform estimates with respect to the Knudsen number epsilon for the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions. Consequently, we prove the convergence to the two-fluid incompressible NSFP as epsilon goes to 0.

• 单位
  武汉大学