In space dimension n < 3, we consider the magnetic Schrödinger Hamiltonian H = -(∇ - iA(x)) 2 and the corresponding Schrödinger equation iτu + Hu=0. ]We show some explicit examples of potentials A, with less than Coulomb decay, for which any solution of this equation cannot satisfy Strichartz estimates, in the whole range of Schrödinger admissibility. © 2011 World Scientific Publishing Company.
Counterexamples to strichartz estimates for the magnetic Schrödinger equation / Fanelli, Luca; Andoni, Garcia. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 13:2(2011), pp. 213-234. [10.1142/s0219199711004245]
Counterexamples to strichartz estimates for the magnetic Schrödinger equation
FANELLI, Luca;
2011
Abstract
In space dimension n < 3, we consider the magnetic Schrödinger Hamiltonian H = -(∇ - iA(x)) 2 and the corresponding Schrödinger equation iτu + Hu=0. ]We show some explicit examples of potentials A, with less than Coulomb decay, for which any solution of this equation cannot satisfy Strichartz estimates, in the whole range of Schrödinger admissibility. © 2011 World Scientific Publishing Company.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
