Pith. sign in

REVIEW

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0906.3382 v2 pith:BQRRMJ55 submitted 2009-06-18 math.AP math-phmath.MP

Scattering for the focusing {dot H}^(1/2)-critical Hartree equation with radial data

classification math.AP math-phmath.MP
keywords equationradialsolutioncriticaldatafocusinghartreenabla
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We investigate the focusing $\dot H^{1/2}$-critical nonlinear Schr\"{o}dinger equation (NLS) of Hartree type $i\partial_t u + \Delta u = -(|\cdot|^{-3} \ast |u|^2)u$ with $\dot H^{1/2}$ radial data in dimension $d = 5$. It is proved that if the maximal life-span solution obeys $\sup_{t}\big\||\nabla|^{{1/2}}u\big\|_2 < \frac{\sqrt{6}}{3} \big\||\nabla|^{{1/2}}Q\big\|_2$, where $Q$ is the positive radial solution to the elliptic equation(\ref{e14}). Then the solution is global and scatters.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.