{"publisher":"European Mathematical Society Publishing House","publication_status":"published","volume":17,"issue":"1","title":"Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation","month":"02","_id":"8499","doi":"10.4171/jems/499","publication_identifier":{"issn":["1435-9855"]},"citation":{"ama":"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","ista":"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.","ieee":"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. European Mathematical Society Publishing House, pp. 71–149, 2015.","chicago":"Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.” Journal of the European Mathematical Society. European Mathematical Society Publishing House, 2015. https://doi.org/10.4171/jems/499.","mla":"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.","short":"M. Guardia, V. Kaloshin, Journal of the European Mathematical Society 17 (2015) 71–149.","apa":"Guardia, M., & Kaloshin, V. (2015). Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. Journal of the European Mathematical Society. European Mathematical Society Publishing House. https://doi.org/10.4171/jems/499"},"type":"journal_article","article_type":"original","oa_version":"None","date_created":"2020-09-18T10:46:50Z","abstract":[{"text":"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.\r\n\r\nWe 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