Blowup for C¹ solutions of compressible Euler equations with time-dependent damping

In this paper, we will show the blowup phenomenon of solutions to the compressible Euler equations with time-dependent damping. Firstly, under the assumptions that the radially symmetric initial data and initial density contains vacuum states, the singularity of the classical solutions will formed in finite time in Rⁿ(n≥2). Furthermore, we can also find a sufficient condition for the functional of initial data such that smooth solution of the irrotational compressible Euler equations with time-dependent damping breaks down in finite time for all kinds of fractional coefficients in Rⁿ(n≥2). Copyright © 2021 by International Press of Boston, Inc. All rights reserved.