论文标题
多线性加权估计和量子Zakharov系统
Multilinear Weighted Estimates and Quantum Zakharov System
论文作者
论文摘要
我们将一维量子Zakharov系统的紧凑型案例视为周期性边界条件的初始问题。在SchrödingerSobolev的规律性非负性的条件下，我们将Bourgain Norm方法应用于某些类似于边界的Sobolev指数的局部适应性较低，以显示低规律性的局部良好性。使用保护定律和能量方法，我们显示了全球良好的良好性，以实现足够的常规初始数据，而没有任何较小的假设。最后，我们在紧凑的时间间隔内将半古典限制显示为$ε\至0 $，而量子扰动在无限的时间间隔中被证明是单数的。
We consider the compact case of one-dimensional quantum Zakharov system, as an initial-value problem with periodic boundary conditions. We apply the Bourgain norm method to show low regularity local well-posedness for a certain class of Sobolev exponents that are sharp up to the boundary, under the condition that Schrödinger Sobolev regularity is non-negative. Using the conservation law and energy method, we show global well-posedness for sufficiently regular initial data, without any smallness assumption. Lastly we show the semi-classical limit as $ε\to 0$ on a compact time interval, whereas the quantum perturbation proves to be singular on an infinite time interval.
