论文标题
具有传输噪声和关键超线性扩散的反应扩散方程：局部良好和积极性
Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity
论文作者
论文摘要
在本文中，我们考虑了一类随机反应扩散方程。我们提供当地适当的性，规律性，爆破标准和解决方案的积极性。这项工作的关键新颖性与使用传输噪声，关键空间和更高级规律性的解决方案的证明有关，即使在非平滑初始数据的情况下也是如此。关键工具是$ l^p（l^q）$ - 理论，最大规律性估计和尖锐的爆炸标准。我们将本文的结果视为建立全球良好性的一般工具箱，以针对大量的实际感兴趣的反应扩散系统，其中许多是完全开放的。在我们的后续工作（Agresti和Veraar：全球存在...）中，本文的结果适用于Lotka-Volterra方程和Brusselator模型的特定情况。
In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions -- even in case of non-smooth initial data. Crucial tools are $L^p(L^q)$-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work (Agresti and Veraar: Global existence ... ), the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.
