Abstract
In this chapter we discuss an initial-boundary value problem for the Navier-Stokes equations for compressible flows in bounded domains with the no-slip boundary conditions for the velocity. We demonstrate the existence of weak solutions that belong to the intermediate regularity class, with strictly positive and uniformly bounded density and Hölder continuous velocity. The result is proved under the assumption that the initial data are close to a static equilibrium.
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Perepelitsa, M. (2018). Weak Solutions for the Compressible Navier-Stokes Equations in the Intermediate Regularity Class. In: Giga, Y., Novotný, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-13344-7_45
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DOI: https://doi.org/10.1007/978-3-319-13344-7_45
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