andaje aanee krutrim vel

haah lekh sthir aanee sthir nasalelya navier-stokes samikarananchya sthanikdrushtya swatantra andajasathi lagoo kelelya velechya vivechanache truti vishleshan pradan karato. sthir kinwa sthir nasalelya navier-stokes samikaran kinwa euler samikaranachya samasyanche nirakaran karnyasathi sanvahan shabdachi nonalinearity hii mukhya samasya aahe. yaa samasyanche nirakaran karnyasathi stokene 'krutrim sankuchitatechi paddhat' samavisht kelee.
navier-stokes samikaran.
sootra _ 1
andaje andaj lavto.
sanvahani sandnya vagaloon navier-stokes samikarananmadhun stoxcha andaj vikasit keela jaato. asampidak pravahatil lahan punarbharan sankhyansathi, haah andaj adhik upayukt aahe. mug asampidit navier stokes samikaran asey lihile jaau shakate-
 sootra _ 2.
yethe rekheey prasar sandnya sanvahan sandnyevar varchasva gajavate.
sanvahan sandnyekade durlaksh karoon sthir samasyemadhye, aaplyala milate-
 sootra _ 3
hii prakriya vaparoon anek pramey siddha kele jaau shakatat.
daab kinwa ghanata sandnya naslyamule satatya aanee gatee samikaranache vighatan hii asampidit pravah samikaranachya samadhanachi mukhya samasya aahe. chorinane daab vichhedan yaa samasyevar upay prastavit keela; yaa drushtikonas krutrim sankuchitata mhanatat.
 sootra _ 4
vareel samikaranat stoke asey gruheet dharato qee, naun-stationary navier stokes samasya sanvadadyachya sthir samasyechya samadhanakade abhisaran karate. haah upay karyavar avalambun rahnar nahee.
jarr heey navier stokes samikaran aanee daab velechya vyutpannasah satatya samikaran asalelya vareel samikaranasathi vaparale gele, tarr uttar mool navier stokes samasyechya sthir samadhanasarkhech asel.
yaa prakriyet krutrim vel hii naveen sandnya t → φ mhanoon dekhil samavisht kelee jaate. krutrim sankuchitata paddhat duheri velechya charan prakriyesah jodali jaate jyamadhye pratyek bhautik velechya tappyat chhadm-velet punaravrutti samavisht asate. heey asampidak pravahachya samasyechya samadhanakade abhisaran sunishchit karate.

