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- W2038492033 abstract "We consider the quintic two-dimensional focusing nonlinear Schrödinger equation iut=−Δu−|u|4u which is L2-supercritical. Even though the existence of finite-time blow-up solutions in the energy space H1 is known, very little is understood concerning the singularity formation. Numerics suggest the existence of a stable blow-up dynamic corresponding to a self-similar blowup at one point in space. We prove the existence of a different type of dynamic and exhibit an open set among the H1-radial distributions of initial data for which the corresponding solution blows up in finite time on a sphere. This is the first result of an explicit description of a blow-up dynamic in the L2-supercritical setting" @default.
- W2038492033 created "2016-06-24" @default.
- W2038492033 creator A5077889771 @default.
- W2038492033 date "2006-08-15" @default.
- W2038492033 modified "2023-10-15" @default.
- W2038492033 title "Existence and stability of a solution blowing up on a sphere for an L2-supercritical nonlinear Schrödinger equation" @default.
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- W2038492033 doi "https://doi.org/10.1215/s0012-7094-06-13421-x" @default.
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