On the decay property of the cubic fourth-order Schrödinger equation

Abstract

In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on ${\mathbb{R}}^d$ ($5\le d\le 8$) enjoys the same (pointwise) decay property as its linear solution does. This result is proved via a bootstrap argument based on the corresponding global result Pausader \cite{Pau1}. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics.

10 pages. Comments are welcome!

References in corpus (2)

• Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case
• Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schrödinger Equations in Multi-dimensional Spaces