{"product_id":"navia-the-1m-fluid-problem-physics-t-shirt","title":"Navia – The $1M Fluid Problem Physics T-Shirt","description":"\u003cp\u003eNavia guards a prize chest beside a swirling river. Inside is one question about smooth flows.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eThe incompressible Navier–Stokes equations describe how water and air move. The Clay Millennium Prize question asks whether, in three dimensions, smooth initial flows always stay smooth, or whether a finite-time singularity can form.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eρ (∂u\/∂t + (u·∇)u) = −∇p + μ ∇²u,   ∇·u = 0\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eρ: density (kg\/m³)\u003c\/li\u003e\n\u003cli\u003eu: flow velocity (m\/s)\u003c\/li\u003e\n\u003cli\u003et: time (s)\u003c\/li\u003e\n\u003cli\u003ep: pressure (Pa)\u003c\/li\u003e\n\u003cli\u003eμ: dynamic viscosity (Pa·s)\u003c\/li\u003e\n\u003cli\u003e∇: spatial derivative (1\/m)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe Clay Mathematics Institute announced the seven Millennium Prize Problems, each worth $1 million, on 24 May 2000.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Navia, the pixel-art character, with the title. Back: the Navier–Stokes equations, the incompressibility condition, the smoothness question and the Clay source. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936664686695,"sku":"16862514682612377644","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936664719463,"sku":"21201482813748323080","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936664752231,"sku":"27965331580637550973","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936664784999,"sku":"33596504963083241622","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936664817767,"sku":"25700000288505576069","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936664850535,"sku":"26931411993129875003","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936664883303,"sku":"40496993900009734539","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936664916071,"sku":"63907195033244825833","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936664948839,"sku":"44448872301826663067","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936664981607,"sku":"60308918712893868053","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936665014375,"sku":"31208176370043887708","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936665047143,"sku":"22524138218628431727","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936665079911,"sku":"16350844520083310070","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936665112679,"sku":"93032210373675824874","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936665145447,"sku":"23139634600021029701","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936665178215,"sku":"27800583061142921210","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/navier-stokes-millennium_front_02_white.png?v=1793595847","url":"https:\/\/pixelatedphysics.com\/nl\/products\/navia-the-1m-fluid-problem-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}