We consider the mixed problem on the exterior of the unit ball in (Formula presented.) for a defocusing Schrödinger equation with a power nonlinearity (Formula presented.) with zero boundary data. Assuming that the initial data are non-radial, sufficiently small perturbations of large radial initial data, we prove that for all powers (Formula presented.) the solution exists for all times, its Sobolev norms do not inflate, and the solution is unique in the energy class.
On the supercritical Schrödinger equation on the exterior of a ball / D'Ancona, P.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 46:8(2021), pp. 1389-1409. [10.1080/03605302.2021.1881111]
On the supercritical Schrödinger equation on the exterior of a ball
D'Ancona P.
2021
Abstract
We consider the mixed problem on the exterior of the unit ball in (Formula presented.) for a defocusing Schrödinger equation with a power nonlinearity (Formula presented.) with zero boundary data. Assuming that the initial data are non-radial, sufficiently small perturbations of large radial initial data, we prove that for all powers (Formula presented.) the solution exists for all times, its Sobolev norms do not inflate, and the solution is unique in the energy class.| File | Dimensione | Formato | |
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