Journal
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 238, Issue 1124, Pages 1-+Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/memo/1124
Keywords
Weak turbulence; finite time blow up; condensation; pulsating solution; energy transfer
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Funding
- DGES Grant [2011-29306-C02-00]
- Basque Government [IT641-13]
- Hausdorff Center for Mathematics of the University of Bonn
- Collaborative Research Center The Mathematics of Emergent Effects (University of Bonn) [DFG SFB 1060]
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We study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrodinger equation. We define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. We also prove the existence of a family of solutions that exhibit pulsating behavior.
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