Timeline for Why can't I get global existence to linear PDE in this way? [closed]
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2014 at 20:20 | history | closed |
Daniel Moskovich Jack Huizenga Ryan Budney Ben Webster♦ |
Needs details or clarity | |
| Jan 23, 2014 at 15:17 | comment | added | michael_carbon | @AthanagorWurlitzer It is "Mathematical Tools for the study of the incompressible Navier-Stokes Equations and Related Models", bottom of page 361. | |
| Jan 23, 2014 at 15:01 | comment | added | username | which book, which page? | |
| Jan 23, 2014 at 14:40 | comment | added | michael_carbon | @AthanagorWurlitzer I understand now that is just local and unsatisfactory in some way. However, in the Section 1.3.6 book by Boyer and Fabrie, this is exactly how they defines a global solution. | |
| Jan 23, 2014 at 14:37 | comment | added | username | (I deleted my earlier comments to clarify the presentation). No, it is not a global solution, it is still a local solution in time. Local means valid on bounded subsets of the domain of interest, which is exactly what your solution is. It does not matter whether $n$ is large or not, it isn't infinite. | |
| Jan 23, 2014 at 14:16 | comment | added | michael_carbon | @MichaelRenardy Please see the edited question, I clarify what I meant to say. | |
| Jan 23, 2014 at 14:15 | comment | added | michael_carbon | @AthanagorWurlitzer Please see my edited question. Sorry for initial bad phrasing. | |
| Jan 23, 2014 at 14:15 | history | edited | michael_carbon | CC BY-SA 3.0 |
added 175 characters in body
|
| Jan 23, 2014 at 11:50 | answer | added | username | timeline score: 3 | |
| Jan 23, 2014 at 11:40 | review | Close votes | |||
| Feb 3, 2014 at 20:24 | |||||
| Jan 23, 2014 at 11:23 | comment | added | Michael Renardy | So your question then is whether $u\in L^2(0,\infty;V)$? In general no, even for ODEs! | |
| Jan 23, 2014 at 11:14 | comment | added | michael_carbon | @AthanagorWurlitzer No I don't assume there is a global solution. Since we have a unique solution of the PDE for each time interval $[0,T]$, it follows that there is a solution $u_{T_1}$ to the PDE on the time interval $[0,T_1]$ where $T_1 > T.$ Then the restriction of $u_{T_1}$ to the interval $[0,T]$ solves the PDE on the interval $[0,T]$. $T_1$ was arbitrary so we can make it as big as we want. | |
| Jan 23, 2014 at 10:42 | history | asked | michael_carbon | CC BY-SA 3.0 |