AI 中文总结
针对确定性框架下反应扩散系统全局经典解存在性的开放问题，该文证明适当输运噪声可使复杂平衡化学反应网络生成时间全局的唯一强解，还能按指定速率增强空间涨落耗散，证明结合了多种分析方法。
AI 中文摘要
化学反应网络产生的反应扩散系统的全局经典解存在性，在确定性框架下仍是一个重大开放问题，尤其针对具有高多项式增长的反应。我们证明，适当选取的、符合物理动机的输运噪声，可为复杂平衡化学反应网络生成唯一的强解，该解在任意高概率下具有时间全局性。这些解对所有θ<1/2都具有C^θ_t C^∞_x中的路径，尤其在空间上是经典的。此外，我们表明，适当的输运噪声可按任意指定的指数速率增强空间涨落的耗散。我们的证明依赖于尺度极限论证、最大L^p(L^q)正则性以及熵-熵耗散估计的结合。
英文摘要
The existence of global classical solutions for reaction-diffusion systems arising from chemical reaction networks remains a major open problem in the deterministic setting, especially for reactions with high polynomial growth. We prove that a suitably chosen, physically motivated transport noise yields unique strong solutions for complex balanced chemical reaction networks that are global in time with arbitrarily high probability. These solutions possess paths in $C^θ_t C^{\infty}_x$ for all $θ<1/2$ and are, in particular, classical in space. Furthermore, we show that a suitable transport noise can enhance the dissipation of spatial fluctuations at an arbitrarily prescribed exponential rate. Our proofs rely on a combination of scaling-limit arguments, maximal $L^p(L^q)$-regularity, and entropy-entropy dissipation estimates.
Comments57 pages, 1 figure
