Global Well-Posedness for the Generalized Fourth-Order Schr\"odinger Equation

Authors

  • Yuzhao Wang

Keywords:

Schr\"odinger Equation, Global well-posedness

Abstract

We study the Generalized Fourth-Order Schr\"odinger Equation $i\partial_t u +\partial_x^4 u + \partial_x (|u|^{2k}u)=0$. With small initial data we prove global well-posedness results in Sobolev spaces $\dot H^{s_k}$. Our proof relies heavily on the method develop by C. E. Kenig, G. Ponce and L. Vege in \cite{KPV93}, which concern with the generalized KdV equations, but the argument is a little different and shorter since we make use of the Christ-Kiselev lemma. DOI: 10.1017/S0004972711003327

Published

2012-04-22

Issue

Section

Articles