We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys....We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys., 2001, 30（4-6）： 507-520]. The decomposition reduces the half-range, two-point boundary value problem into two decoupled initial value problems of the even part and the odd part. Without using a cutoff approximation around zero velocity, we prove that the initial value problem for the even part is well-posed. For the odd part, we prove the uniqueness of the solution in the odd L2-spaee by analyzing the moment system. An example is provided to show that how to use the analysis to obtain the solution of the stationary Wigner equation with inflow boundary conditions.展开更多
The extended magnetohydrodynamic models are derived based on the moment closure of the Vlasov-Maxwell （VM） equations. We adopt the Grad type moment expansion which was firstly proposed for the Boltzmann equation. A ...The extended magnetohydrodynamic models are derived based on the moment closure of the Vlasov-Maxwell （VM） equations. We adopt the Grad type moment expansion which was firstly proposed for the Boltzmann equation. A new regularization method for the Grad＇s moment system was recently proposed to achieve the globally hyperbolicity so that the local well-posedness of the moment system is attained. For the VM equations, the moment expansion of the convection term is exactly the same as that in the Boltzmann equation, thus the new developed regularization applies. The moment expansion of the electromagnetic force term in the VM equations turns out to be a linear source term, which can preserve the conservative properties of the distribution function in the VM equations perfectly.展开更多
文摘We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys., 2001, 30（4-6）： 507-520]. The decomposition reduces the half-range, two-point boundary value problem into two decoupled initial value problems of the even part and the odd part. Without using a cutoff approximation around zero velocity, we prove that the initial value problem for the even part is well-posed. For the odd part, we prove the uniqueness of the solution in the odd L2-spaee by analyzing the moment system. An example is provided to show that how to use the analysis to obtain the solution of the stationary Wigner equation with inflow boundary conditions.
基金The research of Y. Di was supported in part by the National Magnetic Confinement Fusion Science Program （2011GB105003） and the National Natural Science Foundation of China （Grant No. 11271358）. The research of R. Li was supported in part by the Sci-Tech Interdisciplinary Innovation and Cooperation Team Program of the Chinese Academy of Sciences and the National Natural Science Foundation of China （Gra~t Nos. 11325102, 91330205）.
文摘The extended magnetohydrodynamic models are derived based on the moment closure of the Vlasov-Maxwell （VM） equations. We adopt the Grad type moment expansion which was firstly proposed for the Boltzmann equation. A new regularization method for the Grad＇s moment system was recently proposed to achieve the globally hyperbolicity so that the local well-posedness of the moment system is attained. For the VM equations, the moment expansion of the convection term is exactly the same as that in the Boltzmann equation, thus the new developed regularization applies. The moment expansion of the electromagnetic force term in the VM equations turns out to be a linear source term, which can preserve the conservative properties of the distribution function in the VM equations perfectly.
