The problem of existence and smoothness of solutions to the Navier-Stokes equations is one of the seven Millennium Prize Problems in mathematics. Its core question is whether a fluid with normal initial conditions in three-dimensional space will develop blowup phenomena where velocity or pressure becomes infinite during motion, and whether solutions always exist and remain smooth. Based on the author’s original Theory of Infinite Microscopic Hierarchies and Virtual-Real Mass, this paper gives a complete and unified analysis of the problem purely from the physical essence without complex mathematical formulas. Through core laws such as same-level collision, cross-level penetration, pressure difference mechanism, relationship between particle hierarchy and velocity, and internal spatial structure of fluids, it is proved that under conventional flow conditions, fluid particles can neither form extreme pressure difference at black hole level nor achieve high-density fusion conditions at solar core level. The probability of collision and penetration of ultra-microscopic particles is extremely low, and particles only undergo mild same-level collision and velocity redistribution with total motion conserved. Finally, it is essentially concluded that the Navier-Stokes equations in three-dimensional space always admit smooth, finite and stable solutions without blowup or non-smooth behavior. 纳维-斯托克斯方程解的存在性与光滑性问题是七大千禧数学难题之一,核心疑问在于三维空间中初始正常的流体,在运动过程中是否会出现速度、压强无穷大的爆破现象,解是否永远存在且光滑。本文依托作者原创的微观无限层级与虚实质量理论,仅从物理本质出发,不使用复杂数学公式,对该问题进行完整统一解析。通过同级相撞、跨级穿越、压强差机制、粒子层级与速度关系、流体内部空间结构等核心规律,证明流体粒子在常规流动环境中既无法形成黑洞级极端压强,也不具备太阳内核级高密度聚变条件,超微观粒子穿越碰撞概率极低,粒子仅存在温和的同级碰撞与速度重新分配,运动总量守恒。最终从本质上回应了纳维–斯托克斯方程在三维空间中永远存在光滑、有限、稳定的解,不会出现爆破与不光滑现象。
Haigang Geng (Tue,) studied this question.