标题： 关于受空间-时间白噪声导数强迫的Burgers方程摄动的整体唯一解 显示英文标题

标题： Global unique solution to the perturbation of the Burgers' equation forced by derivatives of space-time white noise

摘要： 我们研究了一维Burgers方程，该方程受分数阶导数（阶数为$\frac{1}{2}$）驱动，并作用于空间-时间白噪声上。 基于Allez和Chouk（2015, arXiv:1511.02718 [math.PR]）提出的Anderson-Hamiltonian方法以及Hairer和Rosati（2024, Annals of PDE,\textbf{10}, pp. 1--46）研究的受空间-时间白噪声驱动的二维Navier-Stokes方程的方法，我们证明了其温和解和弱解在整个时间区间上的全局存在性和唯一性。 显示英文摘要

摘要： We consider the one-dimensional Burgers' equation forced by fractional derivative of order $\frac{1}{2}$ applied on space-time white noise. Relying on the approaches of Anderson Hamiltonian from Allez and Chouk (2015, arXiv:1511.02718 [math.PR]) and two-dimensional Navier-Stokes equations forced by space-time white noise from Hairer and Rosati (2024, Annals of PDE, \textbf{10}, pp. 1--46), we prove the global-in-time existence and uniqueness of its mild and weak solutions.