Sur le mouvement d'un liquide visqueux emplissant l'espace

1934/01/01 by Jean Leray · 135 citations
Engineering · #Control and Dynamics of Mobile Robots

paper · pdf · doi:10.1007/bf02547354

Abstract

Introduction. ~ I. La thdorie de la viscositd conduit ~ admettre que les mouvements des liquides visqueux sont regis par les 6quations de N~vier; il est n6cessMre de justifier a posteriori cette hypoth~se eu 6t~blissunt le thdor~me d'existe~ce suiva~t." il existe une solution des 6quations de Navier qui correspond "s un 6tat de vitesse donn~ arbi~rairement s l'instant ini~iM. C'est ce qu'a cherch6 ~ d6montrer M. Oseena; il n'u r6ussi s 6tablir l'existence d'une telle solution que pour une dur6e peut-~tre tr~s br~ve succ6dant ~ l'instunt initiul. On peut v6rifier en outre que l'dnergie cindtique tot~le du liquide reste born~e4; mais il ne semble pas possible de d6duire de ce fuit que le mouvement lui-m~me reste r6gulier; j'ui mSme indiqu6 une raison qui me f~it croire ~ l'existence de mouvements devenunt irrdguliers uu bout d'un temps finiS; je n'ai m~lheureusement p~s rdussi ~ forger un exemple d'une telle singularit6.

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