Boundary-layer phenomena for the cylindrically symmetric Navier-Stokes equations of compressible heat-conducting fluids with large data at vanishing shear viscosity

摘要

This paper concerns the asymptotic behavior of the solution to an initial-boundary value problem of the cylindrically symmetric Navier-Stokes equations with large data for compressible heat-conducting ideal fluids, as the shear viscosity mu goes to zero. A suitable corrector function (the so-called boundary-layer type function) is constructed to eliminate the disparity of boundary values. As by-products, the convergence rates of the derivatives in L-2 are obtained and the boundary-layer thickness (BL-thickness) of the value O(mu(alpha)) with alpha is an element of (0,1/2) is shown by an alternative method, compared with the results proved in Jiang and Zhang (2009 SIAM J. Math. Anal. 41 237-68) and Qin et al (2015 Arch. Ration. Mech. Anal. 216 1049-86).