Abstract
We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of second order in terms of the stream function. It is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently small in C 1,1 and the mass flux is in a suitable regime, there exists a unique global subsonic solution in a suitable class of general nozzles. The assumptions are required to prevent the occurrence of supersonic bubbles inside the nozzles. The asymptotic behavior of subsonic flows at the downstream and upstream, as well as the critical mass flux, has been clarified. © 2012 Society for Industrial and Applied Mathematics.
| Original language | English |
|---|---|
| Pages (from-to) | 2888-2919 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 44 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2012 |
| Externally published | Yes |
Research Keywords
- Asymptotic behavior
- Bernoulli function
- Critical mass flux
- Entropy function
- Existence
- Full Euler equations
- Global subsonic flows
- Infinitely long nozzles
- Reduction
- Second-order nonlinear equations
- Steady flows
- Stream function
- Supersonic bubbles