Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation

  • Marcel Guardia

    Universitat Politècnica de Catalunya, Barcelona, Spain
  • Vadim Kaloshin

    University of Maryland, College Park, United States

Abstract

We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix . Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with -Sobolev norm growing in time.

We establish the existence of solutions with polynomial time estimates. More exactly, there is such that for any we find a solution and a time such that . Moreover, the time satisfies the polynomial bound .

A correction to this paper is available.

Cite this article

Marcel Guardia, Vadim Kaloshin, Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. J. Eur. Math. Soc. 17 (2015), no. 1, pp. 71–149

DOI 10.4171/JEMS/499