We consider a Cauchy problem of an energy-critical fractional Schrodinger equation with Hartree nonlinearity below the energy space. Using randomization of functions on associated with the Wiener decomposition, we prove that the Cauchy problem is almost surely locally well posed. Our result includes the Hartree Schrodinger equation (\( \alpha = 2 \)).
Cite this article
Gyeongha Hwang, Almost Sure Well-Posedness of Fractional Schrödinger Equations with Hartree Nonlinearity. Publ. Res. Inst. Math. Sci. 54 (2018), no. 1, pp. 1–44DOI 10.4171/PRIMS/54-1-1