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arXiv · 1109.5291

Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

N. Tzvetkov·N. Visciglia
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Abstract

Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.

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N. Tzvetkov, N. Visciglia. 2012-07-04. Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. https://arxiv.org/abs/1109.5291

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