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- W4297799144 abstract "We consider the 3d cubic focusing nonlinear Schroedinger equation (NLS) ipartial_t u + Delta u + |u|^2 u=0, which appears as a model in condensed matter theory and plasma physics. We construct a family of axially symmetric solutions, corresponding to an open set in H^1_{axial}(R^3) of initial data, that blow-up in finite time with singular set a circle in xy plane. Our construction is modeled on Raphael's construction cite{R} of a family of solutions to the 2d quintic focusing NLS, ipartial_t u + Delta u + |u|^4 u=0, that blow-up on a circle." @default.
- W4297799144 created "2022-10-01" @default.
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- W4297799144 date "2010-02-11" @default.
- W4297799144 modified "2023-09-25" @default.
- W4297799144 title "A class of solutions to the 3d cubic nonlinear Schroedinger equation that blow-up on a circle" @default.
- W4297799144 doi "https://doi.org/10.48550/arxiv.1002.2407" @default.
- W4297799144 hasPublicationYear "2010" @default.
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