Abstract
We consider the Cauchy problem for the dissipative nonlinear Schrödinger equation with a cubic nonlinear term \(\lambda |u|^2u\), where \(\lambda \in {\mathbb {C}}\) with Im \(\lambda < 0\). We prove the global existence of a unique solution and obtain the uniform estimate in the Gevrey class. Using the uniform regularity estimate, we show the \(L^2\)-decay rate for the solution which has the Gevrey regularity.
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Sato, T. \(L^2\)-decay estimate for the dissipative nonlinear Schrödinger equation in the Gevrey class. Arch. Math. 115, 575–588 (2020). https://doi.org/10.1007/s00013-020-01483-y
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DOI: https://doi.org/10.1007/s00013-020-01483-y