Linear profile decompositions for a family of fourth order Schrödinger equations

Abstract

We establish linear profile decompositions for the fourth order Schrödinger equation and for certain fourth order perturbations of the Schrödinger equation, in dimensions greater than or equal to two. We apply these results to prove dichotomy results on the existence of extremizers for the associated Stein--Tomas/Strichartz inequalities; along the way, we also obtain lower bounds for the norms of these operators.

25 pages. The proof of the old Theorem 7 is clarified and references updated

References in corpus (4)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Mass concentration for the $L^2$-critical Nonlinear Schrödinger equations of higher orders
• The linear profile decomposition for the fourth order Schrödinger equation

Cited by in corpus (3)

• Extremizers for Fourier restriction on hyperboloids
• Some recent progress on sharp Fourier restriction theory
• Sharp Fourier extension on fractional surfaces