论文标题
非线性波方程满足广义无效条件的全球稳定性
Global stability for nonlinear wave equations satisfying a generalized null condition
论文作者
论文摘要
我们证明了满足广义无效条件的非线性波方程系统的全球稳定性。广义无效条件允许其系数有限制$ c^k $规范的空形式。我们证明，使用双线性能量估计和二元性论证，我们证明了衰减和改善良好衍生物的衰减。将此策略与dafermos-rodnianski的$ r^p $估计相结合，然后我们可以证明全球稳定性。证明需要分析与波方程溶液相交的相交的无效超曲面的几何形状。
We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and improved decay of good derivatives using bilinear energy estimates and duality arguments. Combining this strategy with the $r^p$ estimates of Dafermos--Rodnianski then allows us to prove global stability. The proof requires analyzing the geometry of intersecting null hypersurfaces adapted to solutions of wave equations.
