Quasi linear Schrodinger equations I: Small data and quadratic interactions
Quasi linear Schrodinger equations I: Small data and quadratic interactions
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DOI：
10.1016/j.aim.2012.06.010
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发表时间：
2012-10-01
影响因子：
1.7
通讯作者：
Tataru, Daniel
中科院分区：
文献类型：
--
作者：
Marzuola, Jeremy L.;Metcalfe, Jason;Tataru, Daniel
本文证明了一般拟线性Schrodinger方程在低正则Sobolev空间中的局部适定性。这些结果代表了Kenig-Ponce-Vega和Kenig-Ponce-Rolvung-Vega的开创性工作的小数据区域的改进，其中粘性方法用于证明非常高正则性空间中的解的存在性。我们这里的论点完全是分散的。我们证明存在的函数空间是以Mizohata，Ichinose，Doi和其他人（包括作者）的结果为动机构建的。(C)2012 Elsevier Inc. All rights reserved.
In this article, we prove local well-posedness in low-regularity Sobolev spaces for general quasilinear Schrodinger equations. These results represent improvements in the small data regime of the pioneering works by Kenig-Ponce-Vega and Kenig-Ponce-Rolvung-Vega, where viscosity methods were used to prove existence of solutions in very 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. (C) 2012 Elsevier Inc. All rights reserved.