Asymptotic problems in fluid mechanics.

Summary In this thesis, we study (from a mathematical point of view) some asymptotic problems from fluid mechanics. This is motivated by physical as well as numerical reasons: the complete equations of physics are often very complicated and cannot be solved in their entirety, which leads us to consider simplified models that take into account the different scales on which the system can be studied. These models can be justified from a mathematical point of view thanks to convergence theorems when a small parameter tends towards zero. This poses mathematical difficulties, often due to the change in the type of equations, which often correspond to a physical reality: persistence of oscillations, presence of boundary layers. We study three examples which are respectively the passage from the Navier-Stokes equation to the Euler equation in a domain with an edge, the compressible-incompressible boundary of a viscous fluid and finally the study of rotating fluids at high speed.