Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation
Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation
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DOI：
10.1007/s00440-008-0197-z
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发表时间：
2006-10
影响因子：
2
通讯作者：
N. Tzvetkov
中科院分区：
文献类型：
--
作者：
N. Tzvetkov
我们定义了 Gibbs 型的有限 Borel 测度，由圆上负索引的 Sobolev 空间支持。该测度可以被视为有限维测度的极限。这些有限维测量对于常微分方程是不变的，常微分方程对应于本杰明-小野方程在圆上的投影，在三角函数基中的第一个 N,N≥ 1 模式上。
We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE’s which correspond to the projection of the Benjamin–Ono equation, posed on the circle, on the firstN,N≥ 1 modes in the trigonometric bases.