Weak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical Cases

P. I. Plotnikov () and W. Weigant ()
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P. I. Plotnikov: Novosibirsk State University, Mathematical Department
W. Weigant: Universität Bonn, Institute für Angewandte Mathematik

Chapter 31 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 1601-1671 from Springer

Abstract: Abstract In this chapter the compressible Navier-Stokes equations with the critical adiabatic exponents are considered. The crucial point in this situation are new estimates of the Radon measure of solutions. These estimates are applied to the boundary value problem for the compressible Navier-Stokes equations with the critical adiabatic exponents. The existence of weak solutions to 2D isothermal problem is proved. The cancelation of concentrations for 3D nonstationary initial-boundary value problem with the critical adiabatic exponent 3/2 is established.

Date: 2018
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DOI: 10.1007/978-3-319-13344-7_75

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