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Singularity formation for the 1D compressible Euler equations with variable damping coefficient
- Source :
- Nonlinear Analysis. 170:70-87
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- 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.
- Subjects :
- Spacetime
Applied Mathematics
010102 general mathematics
Mathematical analysis
01 natural sciences
Riemann invariant
Euler equations
010101 applied mathematics
symbols.namesake
Singularity
Bounded function
Compressibility
symbols
0101 mathematics
Constant (mathematics)
Analysis
Mathematics
Variable (mathematics)
Subjects
Details
- ISSN :
- 0362546X
- Volume :
- 170
- Database :
- OpenAIRE
- Journal :
- Nonlinear Analysis
- Accession number :
- edsair.doi...........4080a17ed3fbf949050788cd79bf1d79