The compressible Navier–Stokes equations with slip boundary conditions of friction type
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Published:2023-09-02
Issue:5
Volume:74
Page:
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ISSN:0044-2275
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Container-title:Zeitschrift für angewandte Mathematik und Physik
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language:en
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Short-container-title:Z. Angew. Math. Phys.
Author:
Nečasová Šárka,Ogorzaly Justyna,Scherz Jan
Abstract
AbstractWe study a mathematical model of a viscous compressible fluid obeying the slip boundary condition of friction type. We present a notion of weak solutions to this model, in which the momentum equation and the associated energy inequality are combined into a single relation. Moreover, the slip boundary condition of friction type is incorporated into this relation by the use of a boundary integral. Our main result proves the existence of such weak solutions. The proof of this result combines the classical existence theory for the compressible Navier–Stokes equations with an approximation of the aforementioned boundary integral via a convex regularization of the absolute value function.
Funder
Praemium Academiæ of Sarka Necasova
Czech Science Foundation
Grantová Agentura Ceské Republiky
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Physics and Astronomy,General Mathematics
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