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

摘要

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.