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Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation (1109.5291v2)

Published 24 Sep 2011 in math.AP

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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