Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations

Details Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations

2008-05-19

arxiv.org/abs/0805.2925v2

Mathematics

Analysis of PDEs

Scientific paper

In the 2-d setting, given an $H^1$ solution $v(t)$ to the linear Schr\"odinger equation $i\partial_t v +\Delta v =0$, we prove the existence (but not uniqueness) of an $H^1$ solution $u(t)$ to the defocusing nonlinear Schr\"odinger (NLS) equation $i\partial_t u + \Delta u -|u|^{p-1}u=0$ for nonlinear powers $2

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