Singularity formation for the 1D compressible Euler equations with variable damping coefficient
In this paper, we consider some blow-up problems for the 1D Euler equations with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping for the occurrence of the finite time blow-up. In particula...
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| Veröffentlicht in: | Nonlinear analysis 2018-05, Vol.170, p.70-87 |
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| creator | Sugiyama, Yuusuke |
| description | In this paper, we consider some blow-up problems for the 1D Euler equations with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping for the occurrence of the finite time blow-up. In particular, our sufficient conditions ensure that the derivative blow-up occurs in finite time with the solution itself and the pressure bounded. Our method is based on simple estimates with Riemann invariant. Furthermore, we give sharp lower and upper estimates of the lifespan of solutions, when initial data are small perturbations of constant states. |
| doi_str_mv | 10.1016/j.na.2017.12.013 |
| format | Article |
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| source | Elsevier ScienceDirect Journals |
| subjects | Blow-up Cauchy problems Compressibility Damping Decay rate Euler-Lagrange equation Eulers equations Lifespan Mathematical analysis Mathematical problems p-system Singularity formation Spacetime Time dependence |
| title | Singularity formation for the 1D compressible Euler equations with variable damping coefficient |
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