论文标题
QuinticSchrödinger方程弱的湍流状态的奇异性
Singularities in the weak turbulence regime for the quintic Schrödinger equation
论文作者
论文摘要
在本文中，我们讨论了QuinticSchrödinger方程的弱湍流理论引发动力学方程的问题。我们在$ l \ mathbb t $上研究QuinticSchrödinger方程，其中$ l \ gg 1 $，并具有尺寸$ \ varepsilon \ ll 1 $的非线性。我们考虑解决方案的傅立叶系数的相关性$ f（t）$时，$ t = t = t \ varepsilon^{ - 2} $当$ \ varepsilon \ rightarrow 0 $和$ l \ rightarrow \ rightarrow \ infty $。我们的结果可以通过以下方式概括：存在$ \ varepsilon $和$ l $的政权，因此对于$ t $ dyadic，$ f（t）$具有物理文献的预期表格，但$ f $的不一致不连续点。
In this paper, we discuss the problem of derivation of kinetic equations from the theory of weak turbulence for the quintic Schrödinger equation. We study the quintic Schrödinger equation on $L\mathbb T$, with $L\gg 1$ and with a non-linearity of size $\varepsilon\ll 1$. We consider the correlations $f(T)$ of the Fourier coefficients of the solution at times $t = T\varepsilon^{-2}$ when $\varepsilon\rightarrow 0$ and $L\rightarrow \infty$. Our results can be summed up in the following way : there exists a regime for $\varepsilon$ and $L$ such that for $T$ dyadic, $f(T)$ has the form expected from the physics literature, but such that $f$ has an infinite number of discontinuity points.
