论文标题
Wiener Amalgam空间中的Strichartz估计值和非线性波方程的应用
Strichartz estimates in Wiener amalgam spaces and applications to nonlinear wave equations
论文作者
论文摘要
在本文中，我们在Wiener Amalgam空间的上下文中获得了Wave Expagor $ e^{it \ sqrt {-Δ}} $的一些新的Strichartz估计。虽然对于Schrödinger案而言，它对波浪传播器一无所知。这是因为与Schrödinger案不同，没有像繁殖器的整体内核那样的明确公式。为了克服这种缺乏，我们取而代之的是通过将其作为涉及贝塞尔函数的振荡积分来接近内核，然后根据贝塞尔功能的渐近扩展在此类积分中仔细利用在此类积分中的取消。我们的方法也可以应用于Schrödinger案件。我们还获得了一些相应的智障估计值，以给予非线性波方程应用，其中Wiener Amalgam空间作为解决方案空间可以导致对解决方案的局部和全局行为进行更精细的分析。
In this paper we obtain some new Strichartz estimates for the wave propagator $e^{it\sqrt{-Δ}}$ in the context of Wiener amalgam spaces. While it is well understood for the Schrödinger case, nothing is known about the wave propagator. This is because there is no such thing as an explicit formula for the integral kernel of the propagator unlike the Schrödinger case. To overcome this lack, we instead approach the kernel by rephrasing it as an oscillatory integral involving Bessel functions and then by carefully making use of cancellation in such integrals based on the asymptotic expansion of Bessel functions. Our approach can be applied to the Schrödinger case as well. We also obtain some corresponding retarded estimates to give applications to nonlinear wave equations where Wiener amalgam spaces as solution spaces can lead to a finer analysis of the local and global behavior of the solution.
