论文标题
在径向情况下,用于临界非线性波方程的孤子分辨率
Soliton resolution for the energy-critical nonlinear wave equation in the radial case
论文作者
论文摘要
我们考虑了空间尺寸中的径向对称初始数据$ d \ ge 4 $的聚焦非线性波方程。该方程式具有独特的(符号和规模)非平凡的,有限的能源固定解决方案$ W $,称为基态。我们证明,具有有界能量标准的每个有限能溶液会不断地解决渐近脱钩拷贝和游离辐射的有限叠加。
We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $D \ge 4$. This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution $W$, called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.