Steady compressible Navier-Stokes equations with large potential forces via a method of decomposition

Stationary compressible Navier–Stokes equations with inflow condition in domains with piecewise analytical boundaries

“…for some positive constant K. Let the viscosity µ be sufficiently large compared to |Ω|, v L∞ and K. Assume further that (19) holds and the boundary data satisfy following additional assumptions:…”

“…Around the singularity points the boundary is given as a graph x 2 (x 1 ). We assume it satisfies the condition (19) which can be rewritten as…”

“…The result was improved by Novo and Novotný [18] who adopted the nonsteady approach of Feireisl et al [3] and then extended by Mucha and Pokorný to the case of slip boundary conditions in the barotropic case ( [13], [28]) and for the full system including thermal effects [14], see also the result for a system involving radiation effects in [8]. Further improvements in the theory of regular solutions has been made in the nineties ( [17], [19]) but mostly for homogeneous boundary data.…”

Strong solutions to the Navier–Stokes–Fourier system with slip–inflow boundary conditions

“…The existence theory for the steady compressible Navier-Stokes equations in the framework of strong solutions was intensively studied in eighties, see e.g. [20], [21] and many other papers. In the beginning of this century, inspired by the results of P.L.…”

On the Exponential Stability of the Rest State of a Viscous Compressible Fluid

“…Concerning the early literature on this subject, we recall that for a suitable class of barotropic processes, the existence of regular steady solutions with positive densities corresponding to large potential forces and small non-potential forces has been proved in [12]; see also [13]. Moreover, in [15], in the case of viscous heatconducting fluids, the problem of the exponential stability of the rest state has 64 M. Padula JMFM been extensively investigated.…”