The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems

Luigi Ambrosio

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 1, page 25-41
  • ISSN: 0392-4033

Abstract

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n this note we describe some recent developments of the theory of flows associated to vector fields with a low regularity with respect to the spatial variables, for instance with a Sobolev or BV regularity. After the illustration of some applica- tions of this theory to conservation laws and PDE's in fluid dynamics, we give an axiomatic presentation of the problem, based on a probabilistic approach inspired by the work of L.C. Young. In the final part we discuss very recent results on the regularity of the flow itself with respect to the spatial variables.

How to cite

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Ambrosio, Luigi. "The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems." Bollettino dell'Unione Matematica Italiana 10-B.1 (2007): 25-41. <http://eudml.org/doc/290397>.

@article{Ambrosio2007,
abstract = {n this note we describe some recent developments of the theory of flows associated to vector fields with a low regularity with respect to the spatial variables, for instance with a Sobolev or BV regularity. After the illustration of some applica- tions of this theory to conservation laws and PDE's in fluid dynamics, we give an axiomatic presentation of the problem, based on a probabilistic approach inspired by the work of L.C. Young. In the final part we discuss very recent results on the regularity of the flow itself with respect to the spatial variables.},
author = {Ambrosio, Luigi},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {25-41},
publisher = {Unione Matematica Italiana},
title = {The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems},
url = {http://eudml.org/doc/290397},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Ambrosio, Luigi
TI - The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/2//
PB - Unione Matematica Italiana
VL - 10-B
IS - 1
SP - 25
EP - 41
AB - n this note we describe some recent developments of the theory of flows associated to vector fields with a low regularity with respect to the spatial variables, for instance with a Sobolev or BV regularity. After the illustration of some applica- tions of this theory to conservation laws and PDE's in fluid dynamics, we give an axiomatic presentation of the problem, based on a probabilistic approach inspired by the work of L.C. Young. In the final part we discuss very recent results on the regularity of the flow itself with respect to the spatial variables.
LA - eng
UR - http://eudml.org/doc/290397
ER -

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