Counterexamples to Strichartz estimates for the magnetic Schroedinger equation
Abstract
In space dimension n≥3, we consider the magnetic Schr\"odinger Hamiltonian H=-(∇-iA(x))2 and the corresponding Schr\"odinger equation i∂tu+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 Schr\"odinger admissibility.
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