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Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation with a convolution potential

Published 6 Nov 2012 in math.AP and math.DS | (1211.1267v2)

Abstract: Fix $s>1$. Colliander, Keel, Staffilani, Tao and Takaoka proved in \cite{CollianderKSTT10} the existence of solutions of the cubic defocusing nonlinear Schr\"odinger equation in the two torus with $s$-Sobolev norm growing in time. In this paper we generalize their result to the cubic defocusing nonlinear Schr\"odinger equation with a convolution potential. Moreover, we show that the speed of growth is the same as the one obtained for the cubic defocusing nonlinear Schr\"odinger equation in \cite{GuardiaK12}. The results we obtain can deal with any potential in $H{s_0}(\TT2)$, $s_0>0$.

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Authors (1)

  1. Marcel Guardia 

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