论文标题
Quasilinearschrödinger方程III：大数据和短时间
Quasilinear Schrödinger equations III: Large Data and Short Time
论文作者
论文摘要
在本文中，我们证明了在低规范性SOBOLEV空间中的局部适当性，用于大数据一般数据的QuasilIrinearSchrödinger方程，并具有非捕获假设。这些结果代表了作者在以前的作品中考虑的小型数据制度的改进，以及Kenig-Ponce-Vega和Kenig-Ponce-Rolvung-Vega的开创性作品，其中使用粘度方法证明存在用于高规律性空间中局部数据的解决方案。我们这里的论点纯粹是分散的。我们显示的存在的功能空间是由Mizohata，Ichinose，Doi等人（包括作者）的结果构建的。
In this article we prove short time local well-posedness in low-regularity Sobolev spaces for large data general quasilinear Schrödinger equations with a non-trapping assumption. These results represent improvements over the small data regime considered by the authors in previous works, as well as the pioneering works by Kenig-Ponce-Vega and Kenig-Ponce-Rolvung-Vega, where viscosity methods were used to prove existence of solutions for localized data in high regularity spaces. Our arguments here are purely dispersive. The function spaces in which we show existence are constructed in ways motivated by the results of Mizohata, Ichinose, Doi, and others, including the authors.
