Dong Li, Xiaoyi Zhang
Abstract:
For the focusing mass-critical nonlinear Schrodinger equation
, an important problem is to
establish Liouville type results for solutions with ground state mass.
Here the ground state is the positive solution to elliptic equation
.
Previous results in this direction were established in
[12, 16, 17, 29] and they all require
. In this paper, we consider
the rigidity results for rough initial data
for any
.
We show that in dimensions
and under the radial assumption,
the only solution that does not scatter in both time directions
(including the finite time blowup case) must be global and coincide
with the solitary wave
up to symmetries of the equation.
The proof relies on a non-uniform local iteration scheme, the refined
estimate involving the
operator and a new smoothing estimate
for spherically symmetric solutions.
Submitted April 15, 2009. Published June 16, 2009.
Math Subject Classifications: 35Q55.
Key Words: Mass-critical; nonlinear Schrodinger equation.
Show me the PDF file (346 KB), TEX file, and other files for this article.
Dong Li Institute for Advanced Study, Princeton, NJ, 08544, USA email: dongli@ias.edu |
Xiaoyi Zhang Academy of Mathematics and System Sciences, Beijing, China. Institute for Advanced Study, Princeton, NJ, 08544, USA email: xiaoyi@ias.edu |
Return to the EJDE web page