Stability Analysis for the Navier–Stokes Equations of Hydrodynamics

This work is concerned with some comments about the hydrodynamic stability for the Navier–Stokes equations. This is done applying standard methods in the linear and nonlinear regimes for the Maxwell model. We discuss linear spatial and temporal stability for an infinite system described by the Navier–Stokes equations around the equilibrium solution, which corresponds to zero velocity and constant mass density and temperature, under longitudinal perturbations. Also, we show that the nonlinear perturbation analysis for the Navier–Stokes equations may lead to singularities in the solution.