Invariance of the Gibbs measure for the periodic quartic gKdV

@article{Richards2012InvarianceOT,
  title={Invariance of the Gibbs measure for the periodic quartic gKdV},
  author={G. Richards},
  journal={arXiv: Analysis of PDEs},
  year={2012}
}
  • G. Richards
  • Published 2012
  • Mathematics
  • arXiv: Analysis of PDEs
We prove invariance of the Gibbs measure for the (gauge transformed) periodic quartic gKdV. The Gibbs measure is supported on H^s for s<1/2, and the quartic gKdV is analytically ill-posed in this range. In order to consider the flow in the support of the Gibbs measure, we combine a probabilistic argument and the second iteration and construct local-in-time solutions to the (gauge transformed) quartic gKdV almost surely in the support of the Gibbs measure. Then, we use Bourgain's idea to extend… Expand
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