PERIODIC NONLINEAR SCHRODINGER-EQUATION AND INVARIANT-MEASURES
PERIODIC NONLINEAR SCHRODINGER-EQUATION AND INVARIANT-MEASURES
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DOI：
10.1007/bf02099299
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发表时间：
1994-12-01
影响因子：
2.4
通讯作者：
BOURGAIN, J
中科院分区：
文献类型：
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作者：
BOURGAIN, J
本文继续研究了从[LRS]开始的周期NLSE u(t) + u(xx) + u\u\(p-2) = 0 （p小于或等于6）。我们证明了对于完全归一化吉布斯测度e(-beta (phi)) Hd phi(x)的数据集，H(phi) = 1/2积分\phi'\2 - 1/p（经过适当的l2截断），方程是全局适定的。集合和测度在流下是不变的。对KdV方程和修正的KdV方程给出了类似结果的证明。所用的主要成分是[B1]对周期NLS和KdV型方程的一些估计。
In this paper we continue some investigations on the periodic NLSE iu(t) + u(xx) + u\u\(p-2) = 0 (p less-than-or-equal-to 6) started in [LRS]. We prove that the equation is globally wellposed for a set of data phi of full normalized Gibbs measure e(-betaH(phi)) Hd phi(x), H (phi) = 1/2 integral \phi'\2 - 1/p (after suitable L2-truncation). The set and the measure are invariant under the flow. The proof of a similar result for the KdV and modified KdV equations is outlined. The main ingredients used are some estimates from [B1] on periodic NLS and KdV type equations.