We present some results on the blow-up phenomenon for the Schrödinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow-up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetries of the equation and construct a family of explicit blow-up solutions.
Adami, R., Dell'Antonio, G., Figari, R., Teta, A. (2004). Blow-up solutions for the Schr̈dinger equation in dimension three with a concentrated nonlinearity. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 21(1), 121-137 [10.1016/j.anihpc.2003.01.002].
Blow-up solutions for the Schr̈dinger equation in dimension three with a concentrated nonlinearity
ADAMI, RICCARDO;
2004
Abstract
We present some results on the blow-up phenomenon for the Schrödinger equation in dimension three with a nonlinear term supported in a fixed point. We find sufficient conditions for the blow-up exploiting the moment of inertia of the solution and the uncertainty principle. In the critical case, we discuss the additional symmetries of the equation and construct a family of explicit blow-up solutions.
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