## Blowup for $$C^1$$ solutions of compressible Euler equations with time-dependent damping.(English)Zbl 07440970

Summary: 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 $$\mathbb{R}^n(n\geq 2)$$. 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 $$\mathbb{R}^n(n\geq 2)$$.

### MSC:

 35Qxx Partial differential equations of mathematical physics and other areas of application 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B44 Blow-up in context of PDEs 35Q31 Euler equations
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