Math @ Duke
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Publications [#371977] of Alexander J Dunlap
Papers Published
- Dunlap, A, Existence of stationary stochastic Burgers evolutions on $\mathbf{R}^2$ and $\mathbf{R}^3$,
Nonlinearity, vol. 33 no. 12
(October, 2020),
pp. 6480-6501 [doi]
(last updated on 2024/09/17)
Abstract: We prove that the stochastic Burgers equation on $\mathbf{R}^d$, $d < 4$, forced by gradient noise that is white in time and smooth in space, admits spacetime-stationary solutions. These solutions are thus the gradients of solutions to the KPZ equation on $\mathbf{R}^d$ with stationary gradients. The proof works by proving tightness of the time-averaged laws of the solutions in an appropriate weighted space.
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