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- W4378501244 abstract "We build a smooth time-dependent real potential on the two-dimensional torus, decaying as time tends to infinity in Sobolev norms along with all its time derivative, and we exhibit a smooth solution to the associated Schrodinger equation on the two-dimensional torus whose $H^s$ norms nevertheless grow logarithmically as time tends to infinity. We use Fourier decomposition in order to exhibit a discrete resonant system of interactions, which we are further able to reduce to a sequence of finite-dimensional linear systems along which the energy propagates to higher and higher frequencies. The constructions are very explicit and we can thus obtain lower bounds on the growth rate of the solution." @default.
- W4378501244 created "2023-05-27" @default.
- W4378501244 creator A5054012690 @default.
- W4378501244 creator A5077003560 @default.
- W4378501244 date "2023-05-25" @default.
- W4378501244 modified "2023-09-25" @default.
- W4378501244 title "Weakly turbulent solution to Schrodinger equation on the two-dimensional torus with real potential decaying at infinity" @default.
- W4378501244 doi "https://doi.org/10.48550/arxiv.2305.15939" @default.
- W4378501244 hasPublicationYear "2023" @default.
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