论文标题
Euler方程解决方案运算符的无限规范
Infinite norm of the derivative of the solution operator of Euler equations
论文作者
论文摘要
通过一个简单而优雅的论点，我们证明了sobolev space $ h^n $的解决方案操作员的衍生物的规范，沿着$ h^n $中的任何基本解决方案，但不在$ h^n $中，但不在$ h^{n+1} $中。我们还从完全发展的湍流的角度回顾了高雷诺数的Navier-Stokes方程的此结果的对应物。最后，我们提供了一些示例和数值模拟，以显示所谓的粗略依赖对初始数据的更完整的图片。
Through a simple and elegant argument, we prove that the norm of the derivative of the solution operator of Euler equations posed in the Sobolev space $H^n$, along any base solution that is in $H^n$ but not in $H^{n+1}$, is infinite. We also review the counterpart of this result for Navier-Stokes equations at high Reynolds number from the perspective of fully developed turbulence. Finally we present a few examples and numerical simulations to show a more complete picture of the so-called rough dependence upon initial data.
