Growth of Sobolev norms of solutions of linear Schrödinger equations on some compact manifolds

277 Figure l-4 : Evolution de la concentration en ions en fonction de la racine carrée du temps pour l'essai avec renouvellement d’acide à pH 3 des mortiers à base

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It has been known for some time that solutions of linear Schrödinger operators on the torus, with bounded, smooth, time dependent (order zero pseudo-differential) potential,

Our goal here is to show that one may construct periodic solutions of non-linear Schrödinger equations (for large sets of frequencies), using just a standard iterative scheme instead

In this analysis, we present a general approximate control- lability result for infinite dimensional quantum systems when a polarizability term is considered in addition to the

ventilation and wall research house, can be fitted with different heating, cooling and ventilating systems to study and compare their performance in terms of energy

In order to prove of Theorem 1, we will also need another bilinear estimate in X −ρ,b spaces, with negative regularity index − ρ < 0: this gain of space derivative is crucial,

• Even if the equation we study is only quadratic, hence “less nonlinear” in a way than the cubic Szegő equation, it appears to be more turbulent, and the example of the