Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605515956 | ||
| 003 | CHVBK | ||
| 005 | 20210128100711.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0875-9 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0875-9 | ||
| 245 | 0 | 0 | |a Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields |h [Elektronische Daten] |c [Luigi Ambrosio, Maria Colombo, Alessio Figalli] |
| 520 | 3 | |a In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theories for ODE's, by developing a local version of the DiPerna-Lions theory. More precisely, we prove the existence and uniqueness of a maximal regular flow for the DiPerna-Lions theory using only local regularity and summability assumptions on the vector field, in analogy with the classical theory, which uses only local regularity assumptions. We also study the behaviour of the ODE trajectories before the maximal existence time. Unlike the Cauchy-Lipschitz theory, this behaviour crucially depends on the nature of the bounds imposed on the spatial divergence of the vector field. In particular, a global assumption on the divergence is needed to obtain a proper blow-up of the trajectories. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Ambrosio |D Luigi |u Scuola Normale Superiore, Pisa, Italy |4 aut | |
| 700 | 1 | |a Colombo |D Maria |u Scuola Normale Superiore, Pisa, Italy |4 aut | |
| 700 | 1 | |a Figalli |D Alessio |u University of Texas at Austin, Austin, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 1043-1081 |x 0003-9527 |q 218:2<1043 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0875-9 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0875-9 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ambrosio |D Luigi |u Scuola Normale Superiore, Pisa, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Colombo |D Maria |u Scuola Normale Superiore, Pisa, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Figalli |D Alessio |u University of Texas at Austin, Austin, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 1043-1081 |x 0003-9527 |q 218:2<1043 |1 2015 |2 218 |o 205 | ||