Fluid mechanics is one of the main branches in physics with a wide variety of useful applications. A better understanding of the mathematical problems that arise in this discipline is obligatory if it is desired to know and to explain certain phenomena that are exclusive of this branch.
The description of a fluid is governed by the Navier-Stokes equations. This course presents the mathematical models for a homogenous, Newtonian and incompressible fluid. We distinguish between the steady state and the evolution equations. For both cases, we give some very well-known existence and uniqueness results.
The main tool in this study is functional analysis, which combines fixed-point results, Galerkin methods, compactness and Sobolev spaces.
Schedule of the Course 1: