Tuesday, July 11, 2023 - 16:00 in ZiF
Supercritical singular SDEs via energy solutions
A talk in the SPDEs, optimal control and mean field games series by
Nicolas Perkowski from Berlin
| Abstract: |
We consider an SDE with distributional, divergence-free drift $b \in B^{−\gamma}_{p,\infty}$ and additive
Brownian noise and show that for absolutely continuous initial conditions with
$L^2$ density there are unique "energy solutions" (admissible weak solutions) to
such equations, as long as $\gamma < 1$ and $p > 2/(1 − \gamma)$. In particular $b \in L^2$ is
allowed in any dimension. The construction is based on relatively soft estimates
and we need no input from PDE theory beyond $L^2$ energy estimates and the maximum
principle. This is joint work with Ana Djurdjevac, Lukas Gräfner, Xiaohao Ji.
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