Harmoni ity up to rearrangement and isothermal gas

Harmoni ity up to rearrangement and isothermal gas dynami s Yann Brenier Abstra t. The on ept of harmoni (or wave) maps up to rearrangement is introdu ed. A relation is established with the smooth solutions of the isother- mal irrotational invis id gas dynami s equations. On introduit la notion d'appli ation harmonique a rearrangement pres. On etablit un lien ave les solutions regulieres des equations de rivant la dy- namique isotherme des gaz sans vis osite ni tourbillon. 1. Review of some lassi al on epts 1.1. Harmoni (or wave) maps. Let S > 0, T > 0, U =?0; T [?0; S[ and D = T d = (R=Z) d the at torus. A map (t; s) 2 U ! X(t; s) 2 D is usually alled a harmoni map (resp. a wave map) if it is a riti al point of the fun tional Z U 1 2 (j t X(t; s)j 2 + j s X(t; s)j 2 )dtds;(1.1) where = 1 (resp. = 1), with respe t to perturbations with ompa t support in U .

• gas dynami


• isothermal irrotational


• alled minimizing harmoni


• fun tions


• vlasov-poisson equations


• ribing isothermal


• vibrating string


• invis id