BOUNDS ON THE GROWTH OF HIGH SOBOLEV NORMS OF SOLUTIONS TO 2D HARTREE EQUATIONS

作者：Sohinger Vedran^*

来源：Discrete and Continuous Dynamical Systems, 2012, 32(10): 3733-3771.

DOI：10.3934/dcds.2012.32.3733

• Hartree equation
• nonlinear Schrodinger equation
• growth of high Sobolev norms
• resonant decomposition

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we had previously used in [49, 50] to study the analogous problem in one dimension. Since we are working in two dimensions, a more detailed analysis of the resonant frequencies is needed, as was previously used in the work of Colliander-Keel-Staffilani-Takaoka-Tao [19].

• 出版日期2012-10