WELL-POSEDNESS OF WEAK SOLUTIONS TO ELECTRORHEOLOGICAL FLUID EQUATIONS WITH DEGENERACY ON THE BOUNDARY

In this article we study the electrorheological fluid equation ut = div(rho(alpha)vertical bar del u vertical bar(p(x)-2)del v), where rho(x) = dist(x, partial derivative Omega) is the distance from the boundary, p(x) is an element of C-1 ((Omega) over bar), and p(-) = min(x is an element of(Omega) over bar)p(x) > 1 We show how the degeneracy of rho(alpha) on the boundary affects the well-posedness of the weak solutions. In particular, the local stability of the weak solutions is established without any boundary value condition.