Timeline for Regular Lagrangian flow for explicit ODE with discontinuous right-hand side
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 25, 2022 at 8:47 | vote | accept | Riku | ||
| Jul 22, 2022 at 11:44 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Jul 22, 2022 at 11:35 | answer | added | Nicola Gigli | timeline score: 0 | |
| Jul 22, 2022 at 1:53 | comment | added | Iosif Pinelis | In Theorem 3.1 of that paper about the existence (and uniqueness) of a Lagrangian flow, there is the condition that $D\cdot b$ be absolutely continuous with respect to the Lebesgue measure, where $b$ is the right-hand side of the ODE. Here this condition obviously fails to hold, and I think it should not be hard to see that no Lagrangian flow solution exists here. | |
| Jul 21, 2022 at 20:28 | comment | added | Riku | @IosifPinelis L. Ambrosio: Transport equation and Cauchy problem for BV vector fields. Invent. Math., 158 (2004), 227–26 | |
| Jul 21, 2022 at 17:48 | comment | added | Christian Remling | The solution reaches $X=0$ in finite time $t=|x|$, and then the RHS is undefined at $X=0$. | |
| Jul 21, 2022 at 14:16 | comment | added | Iosif Pinelis | Where is it proved that, if the right-hand side is BV, then there exists a regular Lagrangian flow? | |
| Jul 21, 2022 at 13:19 | history | asked | Riku | CC BY-SA 4.0 |