Luca Fanelli, Andoni Garcia
Published 2009-04-07Version 1
In space dimension $n\geq3$, we consider the magnetic Schr\"odinger Hamiltonian $H=-(\nabla-iA(x))^2$ and the corresponding Schr\"odinger equation i\partial_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.
Counterexamples to $ C^{\infty} $ well posedness for some hyperbolic operators with triple characteristics
Viscous hyperstabilization of detonation waves in one space dimension
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension
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