Abstract
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.
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Yoon, G., Yang, SD., Song, M. et al. Time-discretized steady compressible Navier–Stokes equations with inflow and outflow boundaries. Z. Angew. Math. Phys. 64, 1745–1758 (2013). https://doi.org/10.1007/s00033-013-0322-4
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DOI: https://doi.org/10.1007/s00033-013-0322-4