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- W2950583602 abstract "We study the Cauchy problem for the fractional Schr{o}dinger equation $$ ipartial_tu = (m^2-Delta)^fracalpha2 u + F(u) in mathbb{R}^{1+n}, $$ where $ n ge 1$, $m ge 0$, $1 < alpha < 2$, and $F$ stands for the nonlinearity of Hartree type: $$F(u) = lambda (frac{psi(cdot)}{|cdot|^gamma} * |u|^2)u$$ with $lambda = pm1, 0 <gamma < n$, and $0 le psi in L^infty(mathbb R^n)$. We prove the existence and uniqueness of local and global solutions for certain $alpha$, $gamma$, $lambda$, $psi$. We also remark on finite time blowup of solutions when $lambda = -1$." @default.
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- W2950583602 date "2012-09-26" @default.
- W2950583602 modified "2023-09-24" @default.
- W2950583602 title "On the Cauchy problem of fractional Schr{o}dinger equation with Hartree type nonlinearity" @default.
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- W2950583602 doi "https://doi.org/10.48550/arxiv.1209.5899" @default.
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