Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system with given magnetic field

作者：Liao, Jie; Yang, Xiongfeng^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2007, 67(12): 3335-3349.

DOI：10.1016/j.na.2006.10.016

• Vlasov-Poisson-Boltzmann system
• magnetic field
• global existence

This paper considers the Vlasov-Poisson-Boltzmann system with given magnetic field. The global existence of classical solutions was obtained when the initial data is a small perturbation around a global Maxwellian. The proof is based on the theory of compressible Navier-Stokes-Poisson equations with forcing and the macro-microdecomposition of the solution to the Boltzmann equation with respect to the local Maxwellian introduced in [T.-P. Liu, T. Yang, S.-H. Yu, Energy method for the Boltzmann equation, Physica D 188 (3-4) (2004) 178-192] and elaborated in [T. Yang, H.-J. Zhao, A new energy method for the Boltzmann equation, J. Math. Phys. 47 (2006)]. The result shows that the existence of solutions is independent of the magnetic field.

• 出版日期2007-12-15
• 单位上海交通大学