arXiv subjects

Luigi Forcella

Publications and source records attributed to Luigi Forcella.

21 records · Page 2Linked to original sources

arXiv2017

Double Scattering Channels for $1D$ NLS in the Energy Space and its Generalization to Higher Dimensions

We consider a class of $1D$ NLS perturbed with a steplike potential. We prove that the nonlinear solutions satisfy the double scattering channels in the energy space. The proof is based on concentration-compactness/rigidity method. We prove moreover that in dimension higher than one, classical scattering holds if the potential is periodic in all but one dimension and is steplike and repulsive in the remaining one.

math.AP↗

arXiv2017

The electrostatic limit for the 3D Zakharov system

We consider the vectorial Zakharov system describing Langmuir waves in a weakly magnetized plasma. In its original derivation the evolution for the electric field envelope is governed by a Schrödinger type equation with a singular parameter which is usually large in physical applications. Motivated by this, we study the rigorous limit as this parameter goes to infinity. By using some Strichartz type estimates to control separately the fast and slow dynamics in the problem, we show that the evolution of the electric field envelope is asymptotically constrained onto the space of irrotational vector fields.

math.AP↗

arXiv2017

Large data scattering for the defocusing NLKG on waveguide $\mathbb R^d\times\mathbb T$

We consider the pure-power defocusing nonlinear Klein-Gordon equation, in the energy subcritical case, posed on the product space $\mathbb R^d\times \mathbb T$, where $\mathbb T$ is the one-dimensional flat torus. In this framework, we prove that scattering holds for any initial data belonging to the energy space $H^1 \times L^2$ for $1\leq d\leq 4$. The strategy consists in proving a suitable profile decomposition theorem in $\mathbb R^d\times \mathbb T$ to pursue a concentration-compactness \& rigidity method.

math.AP↗