Blowup of classical solutions to the pressureless Euler/isentropic Navier-Stokes equations

摘要

In this paper, we will show the blowup of classical solutions to the Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations in arbitrary dimensions under some restrictions on the initial data. Compared with the degenerate viscosities appeared in the recent work, we consider the constant viscosities, but we can remove the condition that the adiabatic exponent has a upper bound, which was a key constraint in the proof of the blow-up result is based on the construction of some new differential inequalities.