AI 中文总结
该研究针对d≥3的环面上随机抛物-抛物Keller--Segel方程，利用随机极大正则性估计证明其在临界Besov空间中的局部适定性，且初始数据足够小时解的存在时间可任意延长，为相关研讨会报告作出贡献。
AI 中文摘要
我们研究d维环面上的随机抛物-抛物Keller--Segel方程，其中d≥3，且方程定义在标度临界Besov空间中。利用随机极大正则性估计，我们证明了该方程的局部适定性，即存在直至最大存在时间的唯一解。我们表明，只要初始数据在这些临界空间中足够小，存在时间就可以以任意高的概率被任意延长。本文是为Antonio Agresti和Mark Veraar组织的研讨会‘临界空间中的随机偏微分方程’撰写的Oberwolfach报告的贡献部分。
英文摘要
We study stochastic, parabolic-parabolic Keller--Segel equations on the $d$-dimensional torus in scaling critical Besov spaces, for $d \geq 3$. Using stochastic maximal regularity estimates, we prove local well-posedness of the equation, i.e., that there exists a unique solution up to a maximal time of existence. We show that the time of existence can be made arbitrarily large with arbitrarily high probability, provided that the initial data is sufficiently small in these critical spaces. Contribution to the Oberwolfach Report for the Seminar 'Stochastic Partial Differential Equations in Critical Spaces' organized by Antonio Agresti and Mark Veraar.
Comments29 pages. Contribution to the Oberwolfach Report for the Seminar 'Stochastic Partial Differential Equations in Critical Spaces' organized by Antonio Agresti and Mark Veraar
