Timeline for reference for existence and blow up results in transport-like PDEs
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 12, 2014 at 8:04 | answer | added | Willie Wong | timeline score: 4 | |
| May 11, 2014 at 18:26 | comment | added | leo monsaingeon | Viewing the PDE as an abstract ODE in Banach spaces can give a hint/flavour compared to the following usual result for finite dimensional ODE's: if $\frac{dy}{dt}=F(t,y)$ for a 'nice' $F$, then the only possibility for the maximal existence time $T$ to be finite is $\lim\limits_{t\to T^-}|y(t)|=\infty$. Then adapting to infinite dimensional PDE's usually requires to find a suitable functional setting (you mentioned the $C^1$ norm, but weaker Sobolev spaces are also very frequent). Apart from that I'm no expert in transport equations so I don't have a precise reference to point you to, sorry. | |
| May 11, 2014 at 18:10 | review | First posts | |||
| May 11, 2014 at 18:18 | |||||
| May 11, 2014 at 17:52 | history | asked | mm-aops | CC BY-SA 3.0 |