Corpus ID: 119170296

Analysis of a Stratified Kraichnan Flow

@article{Huang2017AnalysisOA,
  title={Analysis of a Stratified Kraichnan Flow},
  author={Jingyu Huang and Davar Khoshnevisan},
  journal={arXiv: Probability},
  year={2017}
}
  • Jingyu Huang, Davar Khoshnevisan
  • Published 2017
  • Mathematics
  • arXiv: Probability
  • We consider the stochastic convection-diffusion equation \[ \partial_t u(t\,,{\bf x}) =\nu\Delta u(t\,,{\bf x}) + V(t\,,x_1)\partial_{x_2}u(t\,,{\bf x}), \] for $t>0$ and ${\bf x}=(x_1\,,x_2)\in\mathbb{R}^2$, subject to $\theta_0$ being a nice initial profile. Here, the velocity field $V$ is assumed to be centered Gaussian with covariance structure \[ \text{Cov}[V(t\,,a)\,,V(s\,,b)]= \delta_0(t-s)\rho(a-b)\qquad\text{for all $s,t\ge0$ and $a,b\in\mathbb{R}$}, \] where $\rho$ is a… CONTINUE READING

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