Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

Details Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

2010-03-30

arxiv.org/abs/1003.5709v3

Mathematics

Analysis of PDEs

36 pages, Improved result

Scientific paper

In this paper, we consider Hartree-type equations on the two-dimensional
torus and on the plane. We prove polynomial bounds on the growth of high
Sobolev norms of solutions to these equations. The proofs of our results are
based on the adaptation to two dimensions of the techniques we previously used
to study analogous problems on $S^1$, and on $\mathbb{R}$.

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