关于一维随机热方程路径适定性的一个注记
A remark on pathwise well-posedness of the 1-$d$ stochastic heat equation
AI总结：
研究圆上带乘性噪声的一维随机热方程路径适定性，结合卷积Young和粗糙积分理论与随机张量估计方法，在Young和粗糙情形下建立其路径适定性，改进前人结果，在粗糙情形获最优结果。
AI中文摘要：
我们研究了在圆上具有乘性噪声的随机热方程（SHE）的路径适定性。通过将Gubinelli和Tindel（2010）引入的卷积Young和粗糙积分理论，与Chapouto及第二和第三作者（2026）引入的用于具有乘性噪声的随机色散偏微分方程路径适定性的随机张量估计方法相结合，我们在Young情形和粗糙情形下都建立了SHE的路径适定性，改进了Gubinelli和Tindel（2010）的结果。特别是在粗糙情形（即时白噪声情形）下，我们的结果涵盖了几乎时空白噪声的情况，从而在单参数粗糙路径框架内建立了最优结果。
英文摘要：
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.
