Shape inverse problem for the two-dimensional unsteady stokes flow

In this article, the shape inverse problem for the two-dimensional unsteady Stokes flow has been presented. We employ Piola transformation to bypass the divergence free condition for the flow and prove the differentiability of the solution to the initial boundary value problem. For the approximate solution of the ill-posed and nonlinear problem, we propose a regularized Gauss-Newton method. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible.