受迫Navier–Stokes流中计算的速度场检测

受迫Navier–Stokes流中计算的速度场检测

Velocity-Field Detection of Computation in Forced Navier–Stokes Flows

OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。

具体内容

稿件对三维不可压Navier–Stokes流构造光滑外力，从静止出发、在任意固定正可计算黏度下，使速度场检测给定机器是否停机。在单位平坦环面上，第三速度分量的逐点测试在固定空间区域使用逐渐缩短的搅拌区间；在ℝ²×𝕋上，积分测试用扩张平移区域阵列与全局有界混合导数外力。垂直速度满足对流–扩散方程，短脉冲控制逐点误差，移动截断控制逃逸质量。摘要未给证明细节，结论待独立审查。

• 构造光滑外力使三维Navier–Stokes速度场检测机器停机
• 单位平坦环面上用逐渐缩短搅拌区间做第三分量逐点测试
• ℝ²×𝕋上用扩张平移区域阵列与全局有界混合导数外力做积分测试

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英文原始摘要

We construct smooth forces for three-dimensional incompressible Navier–Stokes flow, from rest at any fixed positive computable viscosity, whose velocity field detects whether a prescribed machine halts. On the unit flat torus, a pointwise test of the third velocity component uses successively shorter stirring intervals in a fixed spatial region. On $`\mathbb R^2\times\mathbb T`$, an integral test uses an expanding array of translation regions and a force with globally bounded mixed derivatives. The vertical velocity solves an advection–diffusion equation: short bursts control its pointwise error in the first construction, and a moving cutoff controls the total escaped mass in the second.

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