Communications on Pure and Applied Analysis (CPAA)

A decomposition for the Schrödinger equation with applications to bilinear and multilinear estimates
Pages: 627 - 646, Issue 2, March 2018

doi:10.3934/cpaa.2018034      Abstract        References        Full text (440.3K)           Related Articles

Felipe Hernandez - 182 Memorial Dr, Cambridge, MA 02142, United States (email)

1 J. Bennett, A. Carbery and T. Tao, On the multilinear restriction and Kakeya conjectures, Acta Mathematica, 196 (2006), 261-302.       
2 J. Bourgain and C. Demeter, The proof of the $l^2$ decoupling conjecture, arXiv preprint arXiv:1403.5335, 2014.       
3 J. Bourgain and L. Guth, Bounds on oscillatory integral operators based on multilinear estimates, Geometric and Functional Analysis, 21 (2011), 1239-1295.       
4 J. Bourgain, Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity, Intern. Mat. Res. Notices, 5 (1998), 253-283.       
5 J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Almost conservations laws and global rough sol.utions to a nonlinear Schrödinger equation, Math. Res. Letters, 9 (2002), 659-682.       
6 L. R. Ford and D. R. Fulkerson, Maximal flow through a network, Canadian Journal of Mathematics, 8 (1956), 399-404.       
7 L. Guth, A short proof of the multilinear Kakeya inequality, In Mathematical Proceedings of the Cambridge Philosophical Society, volume 158, pages 147-153. Cambridge Univ Press, 2015.       
8 Z. Hani, A bilinear oscillatory integral estimate and bilinear refinements to Strichartz estimates on closed manifolds, Analysis and PDE, 5 (2012), 339-362.       
9 Z. Hani, Global well-posedness of the cubic nonlinear Schrödinger equation on closed manifolds, Communications in Partial Differential Equations, 37 (2012), 1186-1236.       
10 S. Joseph, The max-flow min-cut theorem, 2007.
11 S. Klainerman, I. Rodnianski and T. Tao, A physical space approach to wave equation bilinear estimates, Journal d’Analyse Mathématique, 87 (2002), 299-336.
12 A. Staples-Moore, Network flows and the max-flow min-cut theorem, http://www.math.uchicago.edu/ may/VIGRE/VIGRE2009/REUPapers/Staples-Moore.pdf.
13 T. Tao, A physical space proof of the bilinear Strichartz and local smoothing estimate for the Schrödinger equation, 2010.

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