Communications in Mathematical Sciences
Volume 21 (2023)
The existence and limit behavior of the shock layer for 1D stationary compressible non-Newtonian fluids
Pages: 239 – 253
In this paper, we first define the shock layer to a class of stationary compressible non-Newtonian fluids in one dimension. Then the existence and uniqueness of the shock layer are established. In addition, the limit behavior of the shock layer is analyzed. It is shown that, as the viscosity coefficient and the heat conductivity coefficient vanish, the shock layer to the non-Newtonian fluids tends to a shock wave of the corresponding Euler equations. It is also shown that, as the viscosity coefficient tends to zero, the shock layer goes to a non-viscous shock layer to the non-Newtonian fluids, while as heat-conductivity coefficient tends to zero, the shock layer converges to a thermally non-conducting shock layer to the non-Newtonian fluids.
non-Newtonian fluids, Navier–Stokes equations, Euler equations, shock layer, shock wave
2010 Mathematics Subject Classification
35L67, 74J40, 76A05
Z. Guo was supported by National Natural Science Foundation of China grant 11931013 and GXNSF grant 2022GXNSFDA035078. Y. Su was supported by Northwest University graduate innovation and creativity funds (YZZ17084). J. Liu was supported by National Natural Science Foundation of China grant 11801444.
Received 27 August 2019
Accepted 7 May 2022
Published 27 December 2022