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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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