Oscillatory effects in stochastic PDEs |
Máté Gerencsér, TU Wien (BigBlueButton) |
Friday, 2024-06-14 15:40 |
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I will describe two recent results related to the oscillations of the noise in stochastic PDEs. In the first example, a rougher-than-usual KPZ equation, the fluctuation of the noise is strong enough that on the relevant scale the nonlinearity turns into a new Gaussian noise via a central limit-type theorem. The second example, a 1-dimensional stochastic Allen Cahn equation, is much less singular and a solution theory is fairly unproblematic. Nevertheless, the averaging effects of the noise play a key role in their discretisations: they exhibit four times better temporal pointwise convergence rate than the pointwise regularity of the solution and twice better than the regularity of its single Fourier mode. Based on joint works with Ana Djurdjevac, Helena Kremp, Fabio Toninelli. |