We provide a lower bound for the blow up time of H2 norm entropy solutions inviscid Burgers equation in terms initial datum. This shows an interesting symmetry equation: invariance space under action such nonlinear equation. The argument is based on priori estimates energy and stability type (viscous)

We consider a laminar, steady, two-dimensional flow of an incompressible Newtonian fluid in a channel at high Reynolds number. When the walls are slightly deformed, adverse pressure gradients are generated and separation can occur. The analysis of the flow structure has been done essentially by Smith [7]. Later, a systematic asymptotic analysis has been performed by Saintlos and Mauss [6]. More...

This chapter is devoted to investigations of linear stability of plane-parallel flows of an inviscid nonheat-conducting vibrationally excited gas. Some classical results of the theory of linear stability of ideal gas flows, such as the first and second Rayleigh’s theorems and Howard’s theorem, are generalized. An equation of the energy balance of disturbances is derived, which shows that vibrat...