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 .

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