Maximum decay rate for finite-energy solutions of nonlinear Schrödinger equations

Abstract

We give explicit time lower bounds in the Lebesgue spaces for all nontrivial solutions of nonlin-ear Schrodinger equations bounded in the energy space. The result applies for these equations setin any domain ofRN;including the whole space. This also holds for a large class of nonlinearities,thereby extending the results obtained by Hayashi and Ozawa in [9] and by the author in [2].

Reference

Pascal Bégout, “Maximum decay rate for finite-energy solutions of nonlinear Schrödinger equations”, Differential and Integral Equations, vol. 17, n. 11, 2004, pp. 1411–1422.