22 research outputs found
Structural resolvent estimates and derivative nonlinear Schrodinger equations
A refinement of uniform resolvent estimate is given and several smoothing
estimates for Schrodinger equations in the critical case are induced from it.
The relation between this resolvent estimate and radiation condition is
discussed. As an application of critical smoothing estimates, we show a global
existence results for derivative nonlinear Schrodinger equations.Comment: 21 page
Efeito do alho (Allium sativum Linn.), probiótico e virginiamicina antes, durante e após o estresse induzido pela muda forçada em poedeiras semipesadas
Recent progress in smoothing estimates for evolution equations
This paper is a survey article of results and arguments from several of
authors' papers, and it describes a new approach to global smoothing problems
for dispersive and non-dispersive evolution equations based on ideas of
comparison principle and canonical transforms. For operators of order
satisfying the dispersiveness condition , a range of
smoothing estimates is established. Especially, time-global smoothing estimates
for the operator with lower order terms are the benefit of our new
method. These estimates are known to fail for general non-dispersive operators.
For the case when the dispersiveness breaks, we suggest a modification of the
smoothing estimate. It is equivalent to the usual estimate in the dispersive
case and is also invariant under canonical transformations for the operator
. Moreover, it does continue to hold for a variety of non-dispersive
operators , where may become zero on some set. It is
interesting that this method allows us to carry out a global microlocal
reduction of equations to the translation invariance property of the Lebesgue
measure.Comment: 13 page
Sharp Morawetz estimates
We prove sharp Morawetz estimates - global in time with a singular weight in the spatial variables - for the linear waves. Klein Gordon and Schrodinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.Partially supported by the ERC grant 277778.Peer reviewe