{"id":"openai-math/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows","pdf":"https://github.com/openai/math/blob/main/preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026","tags":["navier-stokes","fluid-dynamics","computability"],"score":0,"title":"Velocity-Field Detection of Computation in Forced Navier–Stokes Flows","domain":"Partial differential equations","family":"376","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Universal computation in forced Navier–Stokes flows"}