论文标题
在能量空间中具有光谱差距的基尔chhoff方程的全球解决方案
Global solutions to the Kirchhoff equation with spectral gap data in the energy space
论文作者
论文摘要
我们证明，经典的双曲线kirchhoff方程可为能量空间中某些类别的初始数据提供全球时间解决方案。我们还表明，有足够的解决方案，以便能量空间中的每个初始基准是两个初始数据的总和。 证明依赖于光谱差距数据的概念，即初始数据的组件消失在频率的大间隔内。我们不会通过线性化方程，因为它在这种较低水平的规律性下没有很好。
We prove that the classical hyperbolic Kirchhoff equation admits global-in-time solutions for some classes of initial data in the energy space. We also show that there are enough such solutions so that every initial datum in the energy space is the sum of two initial data for which a global-in-time solution exists. The proof relies on the notion of spectral gap data, namely initial data whose components vanish for large intervals of frequencies. We do not pass through the linearized equation, because it is not well-posed at this low level of regularity.
