随机Córdoba--Córdoba--Fontelos方程中的伪微分噪声与非局部奇异性形成

中文摘要 AI 辅助

我们研究由乘性Stratonovich噪声驱动的随机Córdoba--Córdoba--Fontelos方程，该噪声振幅允许是一个伪微分算子，其主部近似斜自伴。此类算子包含经典输运噪声，也允许真正的非局部扰动。我们首先在Sobolev空间中建立极大经典解的局部时间理论，证明其存在性、唯一性及爆破准则；接着考虑Stratonovich输运的特殊情形，当全局最大值处的初始非局部陡度足够大时，我们证明有限时间爆破可达到任意高的指定概率，并得到寿命的显式上界；最后，在输运最大值处的非局部陡度发散的事件下，我们建立条件I型上界，且当归一化非局部能量的终端Cesàro平均收敛时，我们还根据其极限值确定了精确的主导阶爆破速率。

英文摘要

We study the stochastic Córdoba--Córdoba--Fontelos equation driven by multiplicative Stratonovich noise. The noise amplitude is allowed to be a pseudo-differential operator whose leading part is nearly skew-adjoint. This class contains classical transport noise and also permits genuinely nonlocal perturbations. We first develop a local-in-time theory for maximal classical solutions in Sobolev spaces, proving existence, uniqueness, and a blow-up criterion. We then consider the special case of Stratonovich transport. For sufficiently large initial nonlocal steepness at a global maximum, we prove finite-time blow-up with arbitrarily high prescribed probability and obtain an explicit upper bound on the lifespan. Finally, on the event that the nonlocal steepness at the transported maximum diverges, we establish a conditional Type-I upper bound. When the terminal Cesàro average of the normalised nonlocal energy converges, we further identify the exact leading-order blow-up rate in terms of its limiting value.

发表机构

• Universidad de La Laguna（拉古纳大学）
• Universidad de Cantabria（坎塔布里亚大学）
• Xi’an Jiaotong-Liverpool University（西交利物浦大学）
• Tianjin University（天津大学）

机构由 AI 辅助整理，请以论文原文为准。