Article ID Journal Published Year Pages File Type
4609504 Journal of Differential Equations 2015 31 Pages PDF
Abstract

In this work we study the well-posedness for the initial value problem associated to a generalized derivative Schrödinger equation for small size initial data in weighted Sobolev space. The techniques used include parabolic regularization method combined with sharp linear estimates. An important point in our work is that the contraction principle is likely to fail but gives us inspiration to obtain certain uniform estimates that are crucial to obtain the main result. To prove such uniform estimates we assume smallness on the initial data in weighted Sobolev spaces.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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