SOLUTIONS OF A 2-DIMENSIONAL GRADE-2 FLUID MODEL WITH A TANGENTIAL BOUNDARY-CONDITION ON NONSMOOTH DOMAINS

In this Note, we construct a solution in H-1 of a two-dimensional grad e-two fluid model, with a non-homogeneous Dirichlet tangential boundar y condition, on a Lipschitz-continuous domain. Existence is proven by splitting the problem into a generalized Stokes problem and a transpor t equation, without restricting the size of the data and the constant parameters of the fluid. In addition, we establish that, if the domain is a curvilinear polygon with curved segments of class C-1.1, each so lution of the grade-two fluid tends to a solution of the Navier-Stokes equations when the material modulus ct tends to zero. To our knowledg e, these results are new. When the domain is a polygon, we show that t he regularity of the solution corresponds to that of a Stokes problem. Uniqueness is established in a convex polygon, for sufficiently small data. (C) Academie des Sciences/Elsevier, Paris.