- 09-94 Thomas Chen and Natasa Pavlovic
- Higher order energy conservation, Gagliardo- Nirenberg-Sobolev inequalities, and global well-posedness for Gross-Pitaevskii hierarchies
(333K, pdf, 23 pages.)
Jun 16, 09
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Abstract. We consider the cubic and quintic Gross-Pitaevskii (GP) hierarchy in $d$ dimensions,
for focusing and defocusing interactions.
We introduce new higher order conserved energy functionals that allow us to prove
global existence and uniqueness of solutions for defocusing
GP hierarchies, with arbitrary initial data in the energy space.
Moreover, we prove generalizations of the Sobolev and Gagliardo-Nirenberg inequalities
for density matrices, which we apply to establish global existence and uniqueness
of solutions for focusing and defocusing GP hierarchies on the $L^2$-subcritical level.