We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein–Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques we previously developed in 2017. In particular, the initial support in the velocity variable does not need to be compact. To control the effect of the large velocities, we identify and exploit several structural properties of the Vlasov equation to prove that the worst nonlinear terms in the Vlasov equation either enjoy a form of the null condition or can be controlled using the wave coordinate gauge. The basic propagation estimates for the Vlasov field are then obtained using only weak interior decay for the metric components. Since some of the error terms are not time-integrable, several hierarchies in the commuted equations are exploited to close the top-order estimates. For the Einstein equations, we use wave coordinates and the main new difficulty arises from the commutation of the energy-momentum tensor, which needs to be rewritten using the modified vector fields.

我们证明了Minkowski空间的全局稳定性，这被视为爱因斯坦-弗拉索夫系统的平凡解。为了估计Vlasov场，我们使用了先前在2017年开发的矢量场和改进的矢量场技术。特别是，速度变量的初始支持不需要紧凑。为了控制大速度的影响，我们确定并利用了Vlasov方程的几个结构特性，以证明Vlasov方程中最差的非线性项要么具有零条件的形式，要么可以使用波坐标仪进行控制。然后，仅使用度量成分的内部弱衰变，即可获得Vlasov场的基本传播估计。由于某些误差项不是时间可积分的，交换方程中的几个层次结构被用来关闭最高阶估计。对于爱因斯坦方程，我们使用波坐标，而主要的新困难来自能量动量张量的换向，需要用修正的矢量场来重写。