Timeline for Prove that the flow of a divergence-free vector field is measure preserving
Current License: CC BY-SA 4.0
7 events
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| Apr 14, 2019 at 11:01 | vote | accept | Riku | ||
| Apr 14, 2019 at 10:29 | comment | added | Skeeve | @Riku I've added the proof of (1). (2) is by definition ($\operatorname{div} (a \mu) = 0$ in the sense of distributions means $\int a \nabla f d \mu = 0$ for any appropriate test function $f$). Concerning (3) I don't claim uniqueness. But note that in the paper you cited only Claim 1 is stated. | |
| Apr 14, 2019 at 10:16 | history | edited | Skeeve | CC BY-SA 4.0 |
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| Apr 12, 2019 at 9:39 | comment | added | Riku | I've also put up a question on a related topic here: mathoverflow.net/questions/327789/… | |
| Apr 11, 2019 at 19:41 | comment | added | Riku | Thank you. 1) How do you prove that the family of measures $\{\mu_t\}_{t\in \mathbb{R}}$ satisfies the continuity equation? 2) Why if $\mu$ is the Lebesgue measure then $\mathrm{div}\,a=0$? 3) Are you claiming that $\mathrm{div} \, a = 0$ is sufficient and necessary if (1) has a unique solution? So, for example, if $a \in L^1_tBV_x$? | |
| Apr 11, 2019 at 19:19 | history | edited | Skeeve | CC BY-SA 4.0 |
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| Apr 11, 2019 at 19:06 | history | answered | Skeeve | CC BY-SA 4.0 |