Timeline for Estimating the flow when we know the vector field
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2012 at 1:59 | comment | added | Michael Renardy | The smooth dependence of a solution of an ODE on initial conditions is a standard topic discussed in introductory textbooks. Voting to close. | |
| Apr 21, 2012 at 18:50 | answer | added | Bazin | timeline score: 1 | |
| Jul 22, 2010 at 21:44 | comment | added | user7807 | Do you want to obtain estimates of the form $| \phi_t(x) | < M$, where $M$ does not depend on $t$? If so, then no: let $v(x) = 1$ on the real line is a counterexample (in this case $\phi_t(x) = x + t$). The above comment by Pietro allows us to obtain estimates of the form $| \phi_t(x) | <Ce^ {M t}$, where $M$ and $C$ do not depend on $x$, and similarly for (spatial) derivatives of $\phi$. | |
| May 30, 2010 at 12:34 | history | edited | Marco Disce | CC BY-SA 2.5 |
some comments
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| May 29, 2010 at 18:26 | comment | added | Pietro Majer | Hi! Have you tried the Gronwall lemma? Also, the derivative wrt x satisfy their usual linear ODE, so you can use the G. lemma also there. | |
| May 29, 2010 at 16:59 | history | asked | Marco Disce | CC BY-SA 2.5 |