Global well-posedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case

作者：Miao Changxing; Xu Guixiang; Zhao Lifeng^*

来源：Journal of Differential Equations, 2009, 246(9): 3715-3749.

DOI：10.1016/j.jde.2008.11.011

• Focusing
• Energy-critical
• Radial
• Fourth-order Schrodinger equations
• Global well-posedness
• Scattering

We consider the focusing energy-critical nonlinear Schrodinger equation Of fourth order iu(t) + Delta(2)u = vertical bar u vertical bar(8/d-4)u, d >= 5, We prove that if a maximal-lifespan radial solution u: I x R d, C obeys sup(t is an element of l) parallel to Delta u(t)parallel to(2) < parallel to Delta W parallel to(2), then it is global and scatters both forward and backward in time. Here W denotes the ground state, which is a stationary solution of the equation. In particular, if a Solution has both energy and kinetic energy less than those of the ground state W at some point in time, then the Solution is global and scatters.

• 出版日期2009-5-1
• 单位北京应用物理与计算数学研究所; 中国科学技术大学