Blow up of classical solutions to the barotropic compressible fluid models of Korteweg type in bounded domains

In this paper, we study the multi-dimensional barotropic compressible Navier-Stokes-Korteweg equations with degenerate coefficients of viscosities and capillary in bounded domains. It is shown that any classical solutions to the initial-boundary-value problem will blow up in finite time, when the initial density admits an isolated mass group. Moreover, a direct application of our result (mu(rho) = mu rho, lambda = 0, alpha = 0) shows that the weak solution obtained by Bresch et al. (2003) cannot be improved to a classical one as long as there is an isolated mass group initially. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

In this study, the multi-dimensional barotropic compressible Navier-Stokes-Korteweg equations with degenerate coefficients of viscosities and capillary in bounded domains were explored. It was found that any classical solutions to the initial-boundary-value problem will blow up in finite time when the initial density contains an isolated mass group. Additionally, it was shown that the weak solution obtained by Bresch et al. (2003) cannot be improved to a classical one in the presence of an isolated mass group initially.