论文标题
将径向非辐射溶液分类为5D非线性波方程
Classification of radial non-radiative solutions to the 5D nonlinear wave equations
论文作者
论文摘要
在这项工作中，我们将所有径向非辐射溶液分类为具有广泛能量临界非线性的5D非线性波方程。我们表明，这样的解决方案总是带有两个特征数字。这些特征数可以通过初始数据的辐射谱或解决方案的渐近行为来确定。此外，两个具有相同特征数的径向弱非辐射溶液必须在其外部区域的重叠部分相互重合。最后，我们为非线性波方程的解决方案的全球行为提供了一些理论的应用。
In this work we classify all radial non-radiative solutions to the 5D nonlinear wave equations with a wide range of energy critical nonlinearity. We show that such a solution always comes with two characteristic numbers. These characteristic numbers can be determined by either the radiation profile of the initial data or the asymptotic behaviour of the solution. In addition, two radial weakly non-radiative solutions with the same characteristic numbers must coincide with each other in the overlap part of their exterior regions. Finally we give a few applications of our theory on the global behaviours of solutions to the nonlinear wave equations.
