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arXiv · 2609.23934

The Neural Forcing for Three-Dimensional Incompressible Navier-Stokes finite time blowup

Beibei Li
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Abstract

We present a two-part neural framework for forced three-dimensional incompressible Navier--Stokes flow. Part~I develops the computational forcing system. A physics-informed neural model generates structured external-force trajectories, candidates are optimized through differentiable PDE rollouts or PPO-Clip, and selected forcings are frozen and checked by independent fixed-force replay. Part~II provides the mathematical certification layer. It separates neural candidate discovery from continuum analysis, derives integrated reciprocal-vorticity criteria that imply Riccati-type growth and finite-time loss of smooth continuation, develops a validated computational-to-continuum transfer strategy, and establishes a conditional positive-probability closure for a nondegenerate neural output law. The proof is complete at the continuum level.

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Beibei Li. 2026-09-20. The Neural Forcing for Three-Dimensional Incompressible Navier-Stokes finite time blowup. https://arxiv.org/abs/2609.23934

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