发表机构
Center for Applied Mathematics & School of Mathematical Sciences, Fudan University; Center for Applied Mathematics, Fudan University（复旦大学应用数学中心与数学科学学院; 复旦大学应用数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文以可读形式呈现OpenAI关于Navier-Stokes方程有限时间爆破手稿中的轮廓构造部分，构造光滑轴对称自相似解，其应力满足可容许锥条件，并引入新线性模型以清晰解释内核构造。
AI 中文摘要
本文以可读且易懂的方式呈现了OpenAI手稿《Navier-Stokes方程的有限时间爆破》中轮廓构造部分的内容。我们认为OpenAI的工作是对Navier-Stokes千禧年奖问题的一项重大进展。所构造的轮廓是光滑且轴对称的。将它们代入Navier-Stokes方程后，产生的残差由一个散度形式的项和一个在固定相似扇区上对$1-t$无穷阶消失的余项组成。相应的应力与径向剪切满足可容许锥条件。应力无需是小量。我们引入了一个新的线性模型，它能更清晰地解释内核构造。振荡脉冲的抵消将在姊妹论文《带光滑外力的Navier-Stokes方程的有限时间爆破，第二部分：通过振荡脉冲进行残差修正》中处理。
英文摘要
This paper gives a readable and accessible version of the profile-construction part of OpenAI's manuscript "Finite Time Blowup for Navier-Stokes". We regard OpenAI's work as a major advance on the Navier-Stokes Millennium Prize Problem. The profiles are smooth and axi-symmetric. Inserting them into the Navier-Stokes equations gives a residual consisting of a divergence-form term and a remainder vanishing to infinite order in $1-t$ on fixed similarity sectors. The associated stress and radial shear satisfy the admissible cone condition. The stress need not be small. We introduce a new linear model that provides a clearer explanation of the inner core construction. The cancellation by oscillatory pulses will be treated in the companion paper "Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part II: Residual Correction via Oscillatory Pulses".
CommentsThis expository article is intended to help the community understand OpenAI's manuscript and will not be submitted to any journal
