Abstract In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.

中文翻译：

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随机 Burgers 方程的存在性、唯一性和数值近似

摘要 在本文中，我们针对一类具有非全局单调非线性的随机偏微分方程 (SPDE) 提出了一个包含温和解的存在性、唯一性、正则性和数值近似的多合一陈述。该结果的证明利用了现有完全显式时空离散近似方案的特性，特别是它满足合适的先验估计这一事实。我们还获得了近似方案对所考虑的 SPDE 的温和解的几乎确定和强收敛。最后，我们将文章的主要结果应用于具有加性时空白噪声的随机 Burgers 方程。