Friday, June 28, 2019 - 14:15 in D5-153
Brownian motion with divergence free drift and its application
A talk in the Oberseminar Analysis series by
Guohuan Zhao
| Abstract: |
I this talk, I plan to investigate the existence and uniqueness for the following SDE:
$$
\mathrm{d} X_{s,t}=b (s,X_{s,t})\mathrm{d} t+\sqrt{2}\mathrm{d} W_t,\ \ X_{s,s}=x,\ \ t\geq s.
$$
Here $W$ is a standard Brownian motion in $\mathbb{R}^d$, $b:\mathbb{R}^d\to \mathbb{R}^d$ is a divergence free drift in $L^q([0,T]; L^p(\mathbb{R}^d))$ and $p,q$ satisfy $\frac{d}{p}+\frac{2}{q}<2$. As an application of our main result, the existence of stochastic Lagrangian particle trajectory for Leray's solution of 3D Navier-Stokes equations will be discussed.
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