Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition

This article studies the solutions in H-1 of a two-dimensional grade-two fl uid model with a non-homogeneous Dirichlet tangential boundary condition, o n a Lipschitz-continuous domain. Existence is proven by splitting the probl em into a generalized Stokes problem and a transport equation, without rest ricting the size of the data and the constant parameters of the fluid. A su bstantial part of the article is devoted to a sharp analysis of this transp ort equation, under weak regularity assumptions. By means of this analysis, it is established that each solution of the grade-two fluid model satisfie s energy equalities and converges strongly to a solution of the Navier-Stok es equations when the normal stress modulus a tends to zero. When the domai n is a polygon, it is shown that the regularity of the solution is related to that of a Stokes problem. Uniqueness is established in a convex polygon, with adequate restrictions on the size of the data and parameters. (C) Els evier, Paris.