Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows

Song Jiang () and Chunhui Zhou ()
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Song Jiang: Institute of Applied Physics and Computational Mathematics
Chunhui Zhou: Southeast University, Department of Mathematics

Chapter 45 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 2549-2594 from Springer

Abstract: Abstract The aim of this chapter is to study the existence of weak solutions to the multidimensional steady isentropic and isothermal compressible Navier-Stokes equations with large external forces. In the past decades, significant progress has been made on the existence of large weak solutions. In this chapter, a brief review of recent existence results on the existence of (renormalized) stationary weak solutions with large external forces will be presented. Different boundary value problems, such as the spatially periodic, slip and Dirichlet boundary value problems, will be investigated, and some related topics such as nonuniqueness, regularity, etc., will also be discussed. The ideas and developed techniques used in analysis will be presented and analyzed, and some open problems will be addressed.

Date: 2018
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DOI: 10.1007/978-3-319-13344-7_63

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