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

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.

preprint2012arXivOpen access
N. TzvetkovN. Visciglia
math.AP
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N. TzvetkovN. Visciglia

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