On the global well-posedness of the quadratic NLS on H^1(T)+L^2(R)
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Contributors
Abstract
We study the one dimensional nonlinear Schrödinger equation with power nonlinearity | u| α-1u for α∈ [1 , 5] and initial data u∈ H1(T) + L2(R). We show via Strichartz estimates that the Cauchy problem is locally well-posed. In the case of the quadratic nonlinearity (α= 2) we obtain global well-posedness in the space C(R, H1(T) + L2(R)) via Gronwall’s inequality.
Details
Original language | English |
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Article number | 11 |
Number of pages | 28 |
Journal | NoDEA Nonlinear Differential Equations and Applications |
Volume | 28 |
Issue number | 2 |
Publication status | Published - 2021 |
Peer-reviewed | Yes |
Keywords
Keywords
- Schrödingergleichung, Wohlgestelltheit