Semiflow Selection to Models of General Compressible Viscous Fluids

We prove the existence of a semiflow selection with range the space of càglàd, i.e. left-continuous and having right-hand limits functions defined on $$[0,\infty )$$ [ 0 , ∞ ) and taking values in a Hilbert space. Afterwards, we apply this abstract result to the system arising from a compressible viscous fluid with a barotropic pressure of the type $$a\varrho ^{\gamma }, \gamma \ge 1$$ a ϱ γ , γ ≥ 1 , with a viscous stress tensor being a nonlinear function of the symmetric velocity gradient.

Stability of the compressible viscous fluid around the plane Couette flow in the presence of a transverse uniform magnetic field

In this paper, we consider the stability of three-dimensional compressible viscous fluid around the plane Couette flow in the presence of a uniform transverse magnetic field and show that the uniform transverse magnetic field has a stabilizing effect on the plane Couette flow. Namely, for a sufficiently large Hartmann number, the compressible viscous plane Couette flow is nonlinear stable for small Mach number and arbitrary Reynolds number so long as the initial perturbation is small enough.