Global in time Strichartz estimates for the fractional Schrodinger equations on asymptotically Euclidean manifolds

Roughly speaking, the main steps of our perturbative approach are the following: choose first a suitable proxy for the main equation (i.e., an integro-partial differential

As far as non- local equations are concerned, continuous dependence estimates for fully nonlinear integro-PDEs have already been derived in [38] in the context of viscosity solutions

Fractional/fractal conservation laws, nonlinear degenerate diffusions, fractional Laplacian, optimal continuous dependence estimates, quantitative continuous depen- dence results..

The main new ingredient in the proofs of Theorems 1.1, 1.2 and 1.4 is a bilinear estimate in the context of Bourgain’s spaces (see for instance the work of Molinet, Saut and

We prove Strichartz type estimates for solutions of the homoge- neous wave equation on Riemannian symmetric spaces.. Our results generalize those of Ginibre and Velo

First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon

We then prove Strichartz estimates for the frac- tional Schr¨ odinger and wave equations on compact Riemannian manifolds without boundary (M, g). This result extends the

Another important problem is to investigate the validity of global-in-time Strichartz estimates for Schr¨ odinger operators with long range potentials with singularities (e.g. in