• DOI:10.1512/IUMJ.2018.67.7365
Corpus ID: 38584306

Existence of invariant measures for the stochastic damped KdV equation

@article{Ekren2015ExistenceOI,
  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},
  year={2015}
}

Ibrahim Ekren, I. Kukavica, M. Ziane

Published 2015

Mathematics

arXiv: Analysis of PDEs

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed

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.