Hydrostatic flows with convex velocity profiles pdf file See final version in Nonlinearity

HOMOGENEOUS HYDROSTATIC FLOWS WITH CONVEX VELOCITY PROFILES Yann Brenier Abstra t We onsider the Euler equations of an in ompressible homogeneous uid in a thin two-dimensional layer 1 < x < +1, 0 < z < , with slip boundary onditions at z = 0, z = and periodi boundary onditions in x. After res aling the verti al variable and letting go to zero, we get the following hydrostati limit of the Euler equations t u + u x u + w z u + x p = 0; (1) x u + z w = 0; z p = 0; (2) supplemented by slip boundary onditions at z = 0 and z = 1 and periodi boundary onditions in x. We show that the orresponding initial-value problem is lo ally, but generally not globally, solvable in the lass of smooth solutions with stri tly onvex horizontal velo ity proles, with onstant slopes at z = 0 and z = 1. Resume On onsidere les equations d'Euler d'un uide in ompressible ho- mogene se mouvant dans une ou he min e 1 < x < +1, 0 < z < , glissant sur les bords z = 0, z = et periodique en x.

• orresponding


• equations


• verti al


• lagrangian sheets


• slip boundary


• horizontal variable


• equations d'euler


• boundary ondi


• ave onditions de glissement en z


• semi-lagrangian equations