Abstract

For some deterministic nonlinear PDEs on the torus whose solutions may blow up in finite time, we show that, under suitable conditions on the nonlinear term, the blow-up is delayed by multiplicative noise of transport type in a certain scaling limit. The main result is applied to the 3D Keller–Segel, 3D Fisher–KPP, and 2D Kuramoto–Sivashinsky equations, yielding long-time existence for large initial data with high probability.

中文翻译：

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运输噪音延迟爆破

摘要

对于某些解可能在有限时间内爆破的环面上的确定性非线性偏微分方程，我们表明，在非线性项的合适条件下，爆破被传输类型的乘法噪声在一定的尺度限制内延迟。主要结果应用于 3D Keller-Segel、3D Fisher-KPP 和 2D Kuramoto-Sivashinsky 方程，产生高概率的大型初始数据的长期存在。