无零条件的Vlasov-波系统在指数动量衰减下的全局动力学
Global dynamics of Vlasov--wave systems without the null condition under exponential momentum decay
AI总结：
该研究针对无零结构的相对论Vlasov-波系统，在两种力场齐次性匹配不同系统的条件下，分别采用拉伸指数、略超指数速度衰减方法，证明其解的全局存在性与修正散射，且说明标量场小性假设不可随意移除。
AI中文摘要：
我们证明了来自小分布函数的无零结构相对论Vlasov-波系统解的全局存在性与修正散射。当力场在动量变量中的齐次性与Vlasov-Maxwell系统相同时，标量场允许取较大值，我们的方法需要拉伸指数速度衰减；当力场的齐次性与Einstein-Vlasov系统匹配时，标量场需取小值且分布函数具有略超指数的速度衰减，这尤其包含麦克斯韦衰减。此外，我们表明即使对于紧支初始数据，标量场的小性假设通常也无法移除。
英文摘要：
We prove global existence and modified scattering for solutions to relativistic Vlasov--wave systems without null structure, arising from small distribution functions. When the homogeneity of the force field in the momentum variable is the same as in the Vlasov-Maxwell system, the scalar fields are allowed to be large and our method requires stretched exponential velocity decay. When it matches that of the Einstein-Vlasov system, the scalar fields are required to be small and the distribution function to have slightly super-exponential velocity decay, which in particular includes Maxwellian decay. Moreover, we show that the smallness assumption on the scalar fields cannot in general be removed, even for compactly supported initial data.
