论文标题
临界径向诺伊曼波的散射在球外
Scattering for critical radial Neumann waves outside a ball
论文作者
论文摘要
我们表明，三维临界散焦点的解决方案通过诺伊曼边界条件在球外部和径向初始数据散射外的诺伊曼边界条件。据我们所知，这是针对Neumann边界条件的非线性波方程散射的第一个结果。我们的证明使用了Kenig和Merle引入的浓度 - 紧凑/刚度的方案，将其扩展到我们的设置，以及所谓的能量方法的通道，以排除紧凑型液体解决方案。对于聚焦方程式，我们还获得了地下态能量以下与$ \ Mathbb r^3 $相同的精确散射/爆炸二分法。
We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. This is to our knowledge the first result of scattering for a nonlinear wave equation with Neumann boundary conditions. Our proof uses the scheme of concentration-compactness/rigidity introduced by Kenig and Merle, extending it to our setup, together with the so-called channels of energy method to rule out compact-flow solutions. We also obtain, for the focusing equation, the same exact scattering/blow-up dichotomy below the energy of the ground-state as in $\mathbb R^3$.
