GLOBAL WELL-POSEDNESS FOR NAVIER-STOKES-DARCY EQUATIONS WITH THE FREE INTERFACE

In this paper, the Navier-Stokes-Darcy equations with the free interface are considered, which model the movement of the sea and the sand in the seafloor or the filtration of blood through the arterial wall. The global well-posedness of the solution perturbed around the constant steady state is obtained and then the almost exponential decay to the constant stationary state is gained. Finally, we present an efficient explicit discrete scheme based on finite-volume method for the free interface system and provide the numerical tests to illustrate the consistency with our analysis result.