Linear and Nonlinear Stability in non-standard Theories of Fluid Dynamics

Abstract

In the last two centuries hydrodynamic stability has been recognized as one of the central problems of uid mechanics. It is concerned with when and how laminar ows break down, their subsequent development, and their eventual transition to turbulence. It has many applications in engineering, in meteorology, in oceanography, in astrophysics and in geophysics. Today, the mathematical, computational and experimental aspects of the stability of laminar uid motions have generated a huge and continuous ow of scienti c researches. We refer to the book by Drazin and Reid [17] and references therein for the stability of hydrodynamic laminar ows and to the treatises by Chandrasekhar [11] and Straughan [87] for the problems related to the onset of convection in a viscous uid in both hydrodynamic and hydromagnetic contexts.