Monday, May 27, 2024 - 14:00 in ZiF, plenary hall
Regularisation by noise for a one-dimensional quasi-linear stochastic heat equation with distributional drift
A talk in the SPDEvent series by
El Mehdi Haress from Université Paris-Saclay, Centrale Supélec
| Abstract: |
We study existence and uniqueness for a one-dimensional quasi-linear stochastic heat equation driven by a space-time white noise and a distributional drift. Assuming that the regularity of the distributional drift is strictly greater than -1, we show that the SPDE has a unique weak solution in a class of Hölder-continuous functions in time. We also prove uniform-in-time bounds on the moments of the solution. The proof rely on stochastic sewing techniques, especially to deduce new regularisation properties of the Ornstein-Uhlenbeck process.
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