{"volume":17,"publication":"Journal of the European Mathematical Society","year":"2015","_id":"8499","status":"public","oa_version":"None","publisher":"European Mathematical Society Publishing House","extern":"1","publication_status":"published","date_updated":"2021-01-12T08:19:41Z","month":"02","publication_identifier":{"issn":["1435-9855"]},"doi":"10.4171/jems/499","article_processing_charge":"No","abstract":[{"lang":"eng","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<T<Kc."}],"type":"journal_article","page":"71-149","intvolume":"        17","article_type":"original","author":[{"last_name":"Guardia","full_name":"Guardia, Marcel","first_name":"Marcel"},{"last_name":"Kaloshin","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-09-18T10:46:50Z","day":"05","language":[{"iso":"eng"}],"title":"Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation","quality_controlled":"1","issue":"1","citation":{"ama":"Guardia M, Kaloshin V. Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. <i>Journal of the European Mathematical Society</i>. 2015;17(1):71-149. doi:<a href=\"https://doi.org/10.4171/jems/499\">10.4171/jems/499</a>","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.","short":"M. Guardia, V. Kaloshin, Journal of the European Mathematical Society 17 (2015) 71–149.","chicago":"Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House, 2015. <a href=\"https://doi.org/10.4171/jems/499\">https://doi.org/10.4171/jems/499</a>.","mla":"Guardia, Marcel, and Vadim Kaloshin. “Growth of Sobolev Norms in the Cubic Defocusing Nonlinear Schrödinger Equation.” <i>Journal of the European Mathematical Society</i>, vol. 17, no. 1, European Mathematical Society Publishing House, 2015, pp. 71–149, doi:<a href=\"https://doi.org/10.4171/jems/499\">10.4171/jems/499</a>.","ieee":"M. Guardia and V. Kaloshin, “Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation,” <i>Journal of the European Mathematical Society</i>, vol. 17, no. 1. European Mathematical Society Publishing House, pp. 71–149, 2015.","apa":"Guardia, M., &#38; Kaloshin, V. (2015). Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Publishing House. <a href=\"https://doi.org/10.4171/jems/499\">https://doi.org/10.4171/jems/499</a>"},"date_published":"2015-02-05T00:00:00Z"}