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Small data global well--posedness and scattering for the inhomogeneous nonlinear Schrödinger equation in Hs(Rn)H^{s} (\mathbb R^{n})

By Jinmyong An and Jinmyong Kim
We consider the Cauchy problem for the inhomogeneous nonlinear Schr\"{o}dinger (INLS) equation \[iu_{t} +\Delta u=|x|^{-b} f\left(u\right), u\left(0\right)=u_{0} \in H^{s} (\mathbb R^{n}),\] where 0<s<min{n,  n2+1}0<s<\min \left\{n,\;\frac{n}{2} +1\right\}, 0<b<min{2,  ns,  1+n2s2}0<b<\min \left\{2,\;n-s,{\rm \; 1}+\frac{n-2s}{2} \right\} and f(u)f\left(u\right) is a nonlinear function that behaves like λuσu\lambda \left|u\right|^{\sigma } u with λC\lambda \in \mathbb C and $\sigma... Show more
July 2, 2021
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Small data global well--posedness and scattering for the inhomogeneous nonlinear Schrödinger equation in $H^{s} (\mathbb R^{n})$
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