Growth of Sobolev Norms in the Cubic Nonlinear Schrodinger Equation with a Convolution Potential
Growth of Sobolev Norms in the Cubic Nonlinear Schrodinger Equation with a Convolution Potential
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DOI：
10.1007/s00220-014-1977-1
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发表时间：
2014-07-01
影响因子：
2.4
通讯作者：
Guardia, Marcel
中科院分区：
文献类型：
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作者：
Guardia, Marcel
修正s > 1。Colliander等人在（Invent Math 181：39-113，2010）中证明了在两个环面中立方散焦非线性薛定谔方程的解的存在性，其s-Sobolev范数随着时间的演变经历任意大的增长。本文将他们的结果推广到具有卷积势的立方离焦非线性薛定谔方程。此外，我们还证明了增长速度与Guardia和Kaloshin（Growth of Sobolev norms in the cubic defocusing Nonlinear Schrodinger Equation.出现在欧洲数学学会杂志，2012年）。
Fix s > 1. Colliander et al. proved in (Invent Math 181:39-113, 2010) the existence of solutions of the cubic defocusing nonlinear Schrodinger equation in the two torus whose s-Sobolev norm undergoes arbitrarily large growth as time evolves. In this paper we generalize their result to the cubic defocusing nonlinear Schrodinger 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 Schrodinger equation in Guardia and Kaloshin (Growth of Sobolev norms in the cubic defocusing Nonlinear Schrodinger Equation. To appear in the Journal of the European Mathematical Society, 2012).