On the unsteady Navier-Stokes equations in a time-moving domain with velocity-pressure boundary conditions (Q1599972)

The authors consider the title problem in weak formulation with sufficiently smooth and small boundary and initial data, with a given pressure, and under the a coercivity condition for the corresponding bilinear operator. First, they study a penalized problem by introducing an appropriate elliptic regularization. Due to the presence of nonlinear terms, standard estimates are not sufficient, and the Frechet-Kolmogorov technique must be used to obtain the existence of a solution for the penalized problem. To derive the existence of a solution to the original problem, the authors cover the noncylindrical domain with Whitney cubes and employ tensorial space-time test functions. Finally, the authors consider time-periodic boundary conditions, and apply the results to a journal bearing flow with circumferential pressure condition.