1,721,036 research outputs found
On the decay of solutions to a class of defocusing NLS
No full textWe consider the defocusing NLS on R^d with pure power nonlinearity
u|u|^\alpha and with initial data in H^1.
We prove that the
L^r-norms of the solutions decay for large time
for any value of \alpha
which is H^1-subcritical.
The main novelty is that we are able to treat the L^2-subcritical case
Asymptotic Lower Bounds for a Class of Schroedinger Equations
No full textWe shall study the Schroedinger equation pertrubed by a potential
V (x) which is real and short–range, whose radial derivative satisfies
some supplementary assumptions. More precisely we shall present a family of
identities satisfied by solutions. As a by–product of these identities we deduce some
uniqueness results for and a lower bound for the so called
local smoothing which becomes an identity in a precise asymptotic sense
A note about the generalized Hardy-Sobolev inequality with potential in L^{p, d}
No full textWe present a generalized version of the Hardy-Sobolev inequality, in which the
homogeneous potential |x|^−α is replaced by any potential V belonging to the Lorentz space
L^n/α,∞(Rn). We show that the best constant in these inequalities is achieved provided that
V ∈ Lnα,d(Rn) where 1 ≤ d < ∞. We also analyze the limit case d = ∞. Finally an
application to a non-linear eigenvalues problem with rough potentials is presente
Small data scattering for the nonlinear Schrödinger equation on product spaces
No full textWe consider the cubic nonlinear Schrödinger equation, posed on R^n × M, where
M is a compact Riemannian manifold and n ≥ 2. We prove that under a suitable
smallness in Sobolev spaces condition on the data there exists a unique global
solution which scatters to a free solution for large times
On the local smoothing for the Schroedinger equation
No full textWe prove a family of identities satisfied by
the solutions to the linear Schroedinger equation. As a consequence of these
identities we shall deduce a lower bound for the local smoothing estimate
and a uniqueness criterion for the solutions to the
Schroedinger equation
- …
