Geodesic
Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
Journal of the European Mathematical Society, Tome 17 (2015) no. 1, pp. 71-149.

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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.
DOI : 10.4171/jems/499
Classification : 35-XX, 37-XX
Mots-clés : Hamiltonian partial differential equations, nonlinear Schrödinger equation, transfer of energy, growth of Sobolev norms, normal forms of Hamiltonian fixed points 
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     author = {Marcel Guardia and Vadim Kaloshin},
     title = {Growth of {Sobolev} norms in the cubic defocusing nonlinear {Schr\"odinger} equation},
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Marcel Guardia; Vadim Kaloshin. Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. Journal of the European Mathematical Society, Tome 17 (2015) no. 1, pp. 71-149. doi : 10.4171/jems/499. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/499/

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