Publications of the Research Institute for Mathematical Sciences


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Volume 54, Issue 1, 2018, pp. 1–44
DOI: 10.4171/PRIMS/54-1-1

Published online: 2018-01-17

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

Gyeongha Hwang[1]

(1) National Taiwan University, Taipei, Taiwan

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 ($\alpha = 2$).

Keywords: Nonlinear Schrödinger equation, fractional Schrödinger equation, Hartree non-linearity, almost sure well-posedness

Hwang Gyeongha: Almost Sure Well-Posedness of Fractional Schrödinger Equations with Hartree Nonlinearity. Publ. Res. Inst. Math. Sci. 54 (2018), 1-44. doi: 10.4171/PRIMS/54-1-1