Time-discretized steady compressible Navier-Stokes equations with inflow and outflow boundaries. (English) Zbl 1280.35100
Summary: The time-discretized steady compressible Navier-Stokes equations in \(n\)-dimensional bounded domains with the velocity specified only at the inflow boundary are considered. The existence and uniqueness of \(L^p\) solutions are proved for \(p>n\). For time-discretized steady flows, results of Kweon and Kellogg and of Kweon and Song are extended in a manner that allows for more general domains and for density-dependent viscosity coefficients. Moreover, we only require \(p>n\) which is a critical barrier in the previous works.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35M10 | PDEs of mixed type |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
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