4 citations · 4 across the 3 of their papers we have counts for
8 papers · 1 filter
On finite time blow-up for a 3D Davey-Stewartson system
Luigi Forcella
We consider the elliptic-elliptic Davey-Stewartson system in the three-dimensional Euclidean space, and we give sufficient conditions for the existence of finite time blow-up solut…
Dynamics of solutions to the Gross-Pitaevskii equation describing dipolar Bose-Einstein condensates
Jacopo Bellazzini, Luigi Forcella
We review some recent results on the long time dynamics of solutions to the Gross-Pitaevskii equation governing non-trapped dipolar Quantum Gases. We describe the asymptotic behavi…
Ground state energy threshold and blow-up for NLS with competing nonlinearities
Jacopo Bellazzini, Luigi Forcella, Vladimir Georgiev
We consider the nonlinear Schrödinger equation with combined nonlinearities, where the leading term is an intracritical focusing power-type nonlinearity, and the perturbation is gi…
Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with nonlinear response
Alex H. Ardila, Van Duong Dinh, Luigi Forcella
We study the asymptotic dynamics for solutions to a system of nonlinear Schrödinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold crite…
Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction
Van Duong Dinh, Luigi Forcella
We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetr…
Regularity results for rough solutions of the incompressible Euler equations via interpolation methods
Maria Colombo, Luigi De Rosa, Luigi Forcella
Given any solution of the Euler equations which is assumed to have some regularity in space - in terms of Besov norms, natural in this context - we show by interpolation method…