Shuanglin Shao

THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS

We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schrodinger equation in high dimensions n ≥ 5, for general L2 initial data in the defocusing case, and for general initial data with Mass less than certain fraction of the Mass of the ground state in the focusing case.

A note on the cone restriction conjecture in the cylindrically symmetric case

In this paper, we present two arguments showing that the classical linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the second follows from a strengthening version of the Hausdorff-Young inequality and the Holder inequality in Lorentz spaces.