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arXiv · 2609.02019

Pseudo-differential noise and nonlocal singularity formation in the stochastic C\'ordoba--C\'ordoba--Fontelos equation

Diego Alonso-Orán·Rafael Granero-Belinchón·Yingting Miao·Hao Tang
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Abstract

We study the stochastic C\'ordoba--C\'ordoba--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 Ces\`aro average of the normalised nonlocal energy converges, we further identify the exact leading-order blow-up rate in terms of its limiting value.

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Diego Alonso-Orán, Rafael Granero-Belinchón, Yingting Miao, Hao Tang. 2026-09-02. Pseudo-differential noise and nonlocal singularity formation in the stochastic C\'ordoba--C\'ordoba--Fontelos equation. https://arxiv.org/abs/2609.02019

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