{"id": "card_floor_navier_stokes", "kind": "note", "title": "The Navier-Stokes chain - from the ideal fluid and the viscous one to the regularity question", "body": "Two trees. Euler's ideal fluid (1757) and Navier's viscous correction (1822) become one in Stokes' derivation from the stress of a continuum (1845): the equations as written today. Then Reynolds' number (1883), Leray's weak solutions for all time (1934), Kolmogorov's scaling (1941), Hopf on domains (1951), Ladyzhenskaya closing two dimensions (1959), Fujita-Kato's strong solutions (1964), partial regularity (Caffarelli-Kohn-Nirenberg 1982), the blow-up criterion (Beale-Kato-Majda 1984), Tao's averaged blow-up (2016). The open end: three dimensions, large data.", "source": {"label": "Narrow Highway - a chain on the one map (operator seed)", "url": "", "ref": "docs/MILLENNIUM_PREPAREDNESS.md", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "floor", "bands": ["floor", "chain", "two trees", "fluids", "navier-stokes", "turbulence", "regularity"], "subject": "The Navier-Stokes chain - from the ideal fluid and the viscous one to the regularity question", "connections": [{"to_card_id": "card_k_floor_of_discovery", "relationship": "part_of", "evidence": "the navier stokes chain rests on the one Floor of Discovery"}, {"to_card_id": "card_chain_euler_1757", "relationship": "has_part", "evidence": "a root of this chain - one of the two trees it began from"}, {"to_card_id": "card_chain_navier_1822", "relationship": "has_part", "evidence": "a root of this chain - one of the two trees it began from"}, {"to_card_id": "card_question_navier_stokes", "relationship": "has_open_end", "evidence": "the open question this chain reaches"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.floor", "facets": {"subject": ["chain", "fluids", "navier-stokes", "regularity", "turbulence", "two trees"]}, "presentation": {"glyph": "•", "kind_label": "floor", "by": "Narrow Highway - a chain on the one map (operator seed)", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_k_floor_of_discovery", "title": "The Floor of Discovery — one floor, and by its design the fear of God", "relationship": "part of", "why": "the navier stokes chain rests on the one Floor of Discovery", "href": "/card/card_k_floor_of_discovery", "resolved": true}, {"id": "card_chain_euler_1757", "title": "Euler 1757 — Principes généraux du mouvement des fluides (E226)", "relationship": "has part", "why": "a root of this chain - one of the two trees it began from", "href": "/card/card_chain_euler_1757", "resolved": true}, {"id": "card_chain_navier_1822", "title": "Navier 1822 — Mémoire sur les lois du mouvement des fluides", "relationship": "has part", "why": "a root of this chain - one of the two trees it began from", "href": "/card/card_chain_navier_1822", "resolved": true}, {"id": "card_question_navier_stokes", "title": "Navier-Stokes existence and smoothness", "relationship": "has open end", "why": "the open question this chain reaches", "href": "/card/card_question_navier_stokes", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_floor_navier_stokes", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_floor_navier_stokes"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}