Global smooth dynamics of a fully ionized plasma with long-range collisions
Global smooth dynamics of a fully ionized plasma with long-range collisions
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DOI：
10.1016/j.anihpc.2013.07.004
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发表时间：
2012-05
影响因子：
1.9
通讯作者：
Renjun Duan
中科院分区：
文献类型：
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作者：
Renjun Duan
电子和离子的完全电离等离子体的运动通常由弗拉索夫-麦克斯韦-朗道系统控制。我们证明了在具有足够光滑性和足够速度权的初始扰动的Sobolev范数和L ~ 2（L × 1）-范数都足够小的条件下，具有长程碰撞核的软势系统的Cauchy问题，特别是经典库仑碰撞系统的Cauchy问题在Maxwell附近的整体解的存在性.作为一个副产品，也得到了解决方案的收敛速度。证明是基于能量方法，通过设计一个新的时间能量范数来捕捉这个复杂系统的不同特征，如R3中宏分量的色散，长程碰撞的奇异性和电磁场的规则性损失。
The motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov–Maxwell–Landau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the long-range collision kernel of soft potentials, particularly including the classical Coulomb collision, provided that both the Sobolev norm and L ξ 2 (L x 1)-norm of initial perturbation with enough smoothness and enough velocity weight is sufficiently small. As a byproduct, the convergence rates of solutions are also obtained. The proof is based on the energy method through designing a new temporal energy norm to capture different features of this complex system such as dispersion of the macro component in R 3, singularity of the long-range collisions and regularity-loss of the electromagnetic field.