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• W2079484994 abstract "We study the global in time existence of small classical solutions to the nonlinear Schrödinger equation with quadratic interactions of derivative type in two space dimensions where λ jk ∈ C. We prove that if the initial data u 0 ∈ H 10 ∩ H 0, 10 satisfy smallness conditions in the weighted Sobolev norm, then the solution of the Cauchy problem (0.1) exists globally in time. Furthermore we prove the existence of the usual scattering states in homogeneous Sobolev space of order one. The proof depends on the energy type estimates, and smoothing property by Doi." @default.
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• W2079484994 date "2012-03-21" @default.
• W2079484994 modified "2023-09-24" @default.
• W2079484994 title "Global Existence for Two Dimensional Quadratic Derivative Nonlinear Schrödinger Equations" @default.
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• W2079484994 doi "https://doi.org/10.1080/03605302.2011.626099" @default.
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