# 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} }

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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