Existence of invariant measures for the stochastic damped KdV equation

  title={Existence of invariant measures for the stochastic damped KdV equation},
  author={Ibrahim Ekren and I. Kukavica and M. Ziane},
  journal={arXiv: Analysis of PDEs},
  • Ibrahim Ekren, I. Kukavica, M. Ziane
  • Published 2015
  • Mathematics
  • arXiv: Analysis of PDEs
  • We address the long time behavior of solutions of the stochastic Korteweg-de Vries equation $ du + (\partial^3_x u +u\partial_x u +\lambda u)dt = f dt+\Phi dW_t$ on ${\mathbb R}$ where $f$ is a deterministic force. We prove that the Feller property holds and establish the existence of an invariant measure. The tightness is established with the help of the asymptotic compactness, which is carried out using the Aldous criterion. 
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