Mathematics > Analysis of PDEs
[Submitted on 1 Mar 2025
]
Title: Global unique solution to the perturbation of the Burgers' equation forced by derivatives of space-time white noise
Title: 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
Abstract: 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.
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