Remarks on blowup of solutions for one‐dimensional compressible Navier–Stokes equations with Maxwell's law

Abstract

In this note, we present some blowup results of solutions to the one-dimensional compressible Navier-Stokes equations with Maxwell's law. First, we improve the blowup result of Hu and Wang [Math. Nachr. 92 (2019), 826-840] with initial density away from vacuum by removing two restrictions. Next, we give a blowup result for the solutions with decay at far fields. Finally, we construct some special analytical solutions to exhibit the blowup or non-blowup phenomena for the relaxed system.