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A remark on pathwise well-posedness of the 1- d stochastic heat equation

Year: 2026

Type: article

Abstract: We study pathwise well-posedness of the stochastic heat equation (SHE) with a multiplicative noise on the circle. By combining the convolution Young and rough integration theory, introduced by Gubinelli and Tindel (2010), with the random tensor estimate approach to pathwise well-posedness of stochastic dispersive PDEs with multiplicative noises, introduced by Chapouto and the second and third authors (2026), we establish pathwise well-posedness of SHE in both the Young and rough cases, improving the results in Gubinelli and Tindel (2010). In particular, in the rough case (= the white-in-time case), our result covers the case of almost space-time white noise, thus establishing an optimal result within the framework of one-parameter rough paths.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2026.10164

Authors: Yufei Shao, Jiawei Li, Tadahiro Oh

Institutions: Beijing Institute of Technology, Maxwell Institute for Mathematical Sciences, University of Edinburgh

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W7208788618

FWCI:

Cites: 15

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