Analysis demonstrates global existence and uniqueness of mild and weak solutions in Burgers' equation, indicating significant advances in mathematical understanding.
We consider the one-dimensional Burgers' equation forced by fractional derivative of order 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, 10, pp. 1--46), we prove the global-in-time existence and uniqueness of its mild and weak solutions.
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Kazuo Yamazaki (2025) studied this question.
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