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Continuous dependence of the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation in \(H^{s} (\mathbb R^{n} )\)

By Jinmyong An and others
We consider the Cauchy problem for the inhomogeneous nonlinear Schr\"{o}dinger (INLS) equation \[iu_{t} +\Delta u=|x|^{-b} f(u),\;u(0)\in H^{s} (\mathbb R^{n} ),\] where \(n\in \mathbb N\), \(0<s<\min \{ n,\; 1+n/2\} \), \(0<b<\min \{ 2,\;n-s,\;1+\frac{n-2s}{2} \} \) and \(f(u)\) is a nonlinear function that behaves like \(\lambda \left|u\right|^{\sigma } u\) with \(\sigma>0\) and... Show more
July 2, 2021
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Continuous dependence of the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation in $H^{s} (\mathbb R^{n} )$
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