From two species Vlasov-Maxwell-Boltzmann system to magnetohydrodynamics system
arXiv:2104.01843
Abstract
In this work, the magnetohydrodynamics system is formally derived from two species Vlasov-Maxwell-Boltzmann system. By employing the hypocoercivity of the linear Boltzmann operator and overcoming the difficulties resulting from the singular Lorentz term, we first obtain the uniform estimates of solutions with respect to the Knudsen number and then derive the magnetohydrodynamics system from the dimensionless Valsov-Maxwell-Boltzmann system.
References in corpus (7)
- Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
- The Vlasov-Maxwell-Boltzmann System in The Whole Space
- From the Boltzmann equation to the incompressible Navier-Stokes equations on the torus: a quantitative error estimate
- From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law: convergence for classical solutions
- From Vlasov-Poisson-Boltzmann system to incompressible Navier-Stokes-Fourier-Poisson system: convergence for classical solutions
- Sensitivity analysis and incompressible Navier-Stokes-Poisson limit of Vlasov-Poisson-Boltzmann equations with uncertainty
- The diffusive limits of two species Vlasov-Maxwell-Boltzmann equations