On the blow‐up phenomena of the compressible Navier‐Stokes‐Korteweg system with degenerate viscosity

Abstract

In this paper, we study the blow-up phenomena of classical solutions to the compressible Navier-Stokes-Korteweg system with degenerate viscosity in arbitrary dimensions. Motivated by the previous work, we obtain the upper and lower decay rates of the internal energy. Furthermore, the results of blow-up phenomena do not require that the initial data have compact support or contain vacuum in any finite region.