Random data Cauchy problem for supercritical Schrödinger equations

We proved the local well-posedness for the power-type nonlinear semi-relativistic or half- wave equation (NLHW) in Sobolev spaces. Our proofs mainly base on the contraction map-

We demonstrate how to set up a scattering framework for equations of this type, including appropriate decay estimates of the free time evolution and the construction of wave

Tzvetkov, Random data Cauchy theory for supercritical wave equations I: Local existence theory, Invent.. Tzvetkov, Random data Cauchy theory for supercritical wave equations II:

Let us mention that local existence results in the spaces X k ( R d ), k > d/2, were already proved by Gallo [6], and that a global existence result in X 2 ( R 2 ) has been

In this section we show global existence of the solution for any initial datum in the case of repulsive or weakly attractive interactions, i.e.. The result is proven in the

Dans cet article nous considerons une version non lineaire de 1’equation de Wheeler-DeWitt simplifiee qui decrit le modele de mini- superespace pour la fonction d’onde

We prove the existence of global weak solutions by a compactness method and, under stronger assumptions, the uniqueness.. of those solutions, thereby

Key words : Nonlinear wave equations, Cauchy problem, Strichartz’ estimate, minimal regularity, homogeneous Besov