Stokes problem of the cornered domain in the plane

摘要

The regularity problem of the Stokes equations for the domain with corner in the plane is solved by using the single layer potential. Because of singular behavior of solutions near corner, the kernel functions of the integral equations become complicated Hardy kernels. Our main concern is the existence of solutions for the L1p class data. It turns out that there are two singular L1p classes in which the integral equations fail to have solutions. Here, we use the Mellin operator and symbol computation to solve this problem