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Existence of stationary stochastic Burgers evolutions on R 2 and R 3 *
Nonlinearity ( IF 1.7 ) Pub Date : 2020-10-23 , DOI: 10.1088/1361-6544/aba50a
Alexander Dunlap

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.

中文翻译:

R 2 和 R 3 上的平稳随机 Burgers 演化的存在 *

我们证明了 $\mathbf{R}^{d}$, $d<4$ 上的随机 Burgers 方程,由时间上为白色且空间上平滑的梯度噪声强制,承认时空平稳解。因此,这些解是具有平稳梯度的 $\mathbf{R}^{d}$ 上 KPZ 方程的解的梯度。该证明的工作原理是在适当的加权空间中证明解的时间平均定律的紧密性。
更新日期:2020-10-23
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