二维量子流体力学系统
The Quantum Hydrodynamics system in two space dimensions
摘要：
本文在能量空间中研究了二维量子流体力学系统弱解的整体存在性。我们不需要对初始数据进行任何额外的规则性和/或小性假设。我们的方法取代了WKB形式主义的极式分解理论，这是不受真空区域的存在。这样，我们建立了一个自洽的理论，只基于粒子密度和电流密度，它不需要定义速度场的节点区域。本文中使用的数学技术是基于均匀（相对于近似参数）的Eschenhartz估计和局部平滑属性。
英文摘要：
In this paper we study global existence of weak solutions for the Quantum Hydrodynamics System in 2-D in the space of energy. We do not require any additional regularity and/or smallness assumptions on the initial data. Our approach replaces the WKB formalism with a polar decomposition theory which is not limited by the presence of vacuum regions. In this way we set up a self consistent theory, based only on particle density and current density, which does not need to define velocity fields in the nodal regions. The mathematical techniques we use in this paper are based on uniform (with respect to the approximating parameter) Strichartz estimates and the local smoothing property.
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