Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation

M. Guardia, V. Kaloshin, Journal of the European Mathematical Society 17 (2015) 71–149.

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Journal Article | Published | English
Author
Guardia, Marcel; Kaloshin, VadimIST Austria
Abstract
We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix s>1. Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with s-Sobolev norm growing in time. We establish the existence of solutions with polynomial time estimates. More exactly, there is c>0 such that for any K≫1 we find a solution u and a time T such that ∥u(T)∥Hs≥K∥u(0)∥Hs. Moreover, the time T satisfies the polynomial bound 0<T<Kc.
Publishing Year
Date Published
2015-02-05
Journal Title
Journal of the European Mathematical Society
Volume
17
Issue
1
Page
71-149
ISSN
IST-REx-ID

Cite this

Guardia M, Kaloshin V. Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. Journal of the European Mathematical Society. 2015;17(1):71-149. doi:10.4171/jems/499
Guardia, M., & Kaloshin, V. (2015). Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. Journal of the European Mathematical Society, 17(1), 71–149. https://doi.org/10.4171/jems/499
Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.” Journal of the European Mathematical Society 17, no. 1 (2015): 71–149. https://doi.org/10.4171/jems/499.
M. Guardia and V. Kaloshin, “Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation,” Journal of the European Mathematical Society, vol. 17, no. 1, pp. 71–149, 2015.
Guardia M, Kaloshin V. 2015. Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. Journal of the European Mathematical Society. 17(1), 71–149.
Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.” Journal of the European Mathematical Society, vol. 17, no. 1, European Mathematical Society Publishing House, 2015, pp. 71–149, doi:10.4171/jems/499.

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