标题： 斯特里哈茨估计和相对论Vlasov-Maxwell系统的矩界 第I部分。 $2$维和$2\frac 12$维的情况 显示英文标题

标题： Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system I. The $2$-D and $2\frac 12$-D cases

摘要： 考虑具有任意大小初始数据的相对论Vlasov-Maxwell系统。 在二维和二维半情况下，Glassey-Schaeffer（1997, 1998, 1998）证明了对于具有紧支撑动量的光滑初始数据，该系统存在唯一的全局经典解。 在本工作中，我们不假设初始数据具有紧支撑动量，而是仅要求数据在动量空间中具有多项式衰减。 在2D和$2\frac 12$D情况下，我们证明了由此类初始数据产生的解的全局存在性、唯一性和正则性。 为此，我们使用Strichartz估计，并证明解的适当矩保持有界。 此外，我们获得了电磁场的$L^\infty_x$范数的时间增长相较于Glassey-Schaeffer的轻微改进。 显示英文摘要

摘要： Consider the relativistic Vlasov-Maxwell system with initial data of unrestricted size. In the two dimensional and the two and a half dimensional cases, Glassey-Schaeffer (1997, 1998, 1998) proved that for regular initial data with compact momentum support this system has unique global in time classical solutions. In this work we do not assume compact momentum support for the initial data and instead require only that the data have polynomial decay in momentum space. In the 2D and the $2\frac 12$D cases, we prove the global existence, uniqueness and regularity for solutions arising from this class of initial data. To this end we use Strichartz estimates and prove that suitable moments of the solution remain bounded. Moreover, we obtain a slight improvement of the temporal growth of the $L^\infty_x$ norms of the electromagnetic fields compared to Glassey-Schaeffer.