Almost Sure Well-Posedness of Fractional Schrödinger Equations with Hartree Nonlinearity

Abstract

We consider a Cauchy problem of an energy-critical fractional Schrodinger equation with Hartree nonlinearity below the energy space. Using randomization of functions on $\mathbb R^d$ associated with the Wiener decomposition, we prove that the Cauchy problem is almost surely locally well posed. Our result includes the Hartree Schrodinger equation (\alpha = 2).