ABSTRACT
In this note, we summarize some results concerning some asymptotic problems coming from fluid mechanics. These asymptotic problems arise when a dimensionless parameter ε goes to zero in an equation describing the motion of some type of fluid (or any other physical system). Physically, this allows a better knowledge of the prevailing phenomenon when this parameter is small. This small parameter usually describes a physical reality. For instance, a slightly compressible fluid is characterized by a low Mach number, whereas a slightly viscous fluid is characterized by a high Reynolds number (which means a low viscosity). In many cases, we have different small parameters (we can be in presence of a slightly compressible and slightly viscous fluid in the same time). Depending on the way these small parameters go to zero, we can recover different systems at the limit. For instance, if ε, δ, ν, η ≪ 1, the limit system can depend on the magnitude of the ratio of ε/δ….
