On the Loss of Continuity for Super-Critical Drift-Diffusion Equations

Luis Silvestre; Vlad Vicol; Andrej Zlatoš

doi:10.1007/s00205-012-0579-3

On the Loss of Continuity for Super-Critical Drift-Diffusion Equations

Luis Silvestre, Vlad Vicol, Andrej Zlatoš

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts, we prove that solutions satisfy a modulus of continuity depending only on the local L¹ norm of the drift, which is a super-critical quantity.

Original language	English (US)
Pages (from-to)	845-877
Number of pages	33
Journal	Archive for Rational Mechanics and Analysis
Volume	207
Issue number	3
DOIs	https://doi.org/10.1007/s00205-012-0579-3
State	Published - Mar 2013

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

Access to Document

10.1007/s00205-012-0579-3

Cite this

@article{5e67bd6df88143adaf534d951786927c,

title = "On the Loss of Continuity for Super-Critical Drift-Diffusion Equations",

abstract = "We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts, we prove that solutions satisfy a modulus of continuity depending only on the local L1 norm of the drift, which is a super-critical quantity.",

author = "Luis Silvestre and Vlad Vicol and Andrej Zlato{\v s}",

year = "2013",

month = mar,

doi = "10.1007/s00205-012-0579-3",

language = "English (US)",

volume = "207",

pages = "845--877",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - On the Loss of Continuity for Super-Critical Drift-Diffusion Equations

AU - Silvestre, Luis

AU - Vicol, Vlad

AU - Zlatoš, Andrej

PY - 2013/3

Y1 - 2013/3

N2 - We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts, we prove that solutions satisfy a modulus of continuity depending only on the local L1 norm of the drift, which is a super-critical quantity.

AB - We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts, we prove that solutions satisfy a modulus of continuity depending only on the local L1 norm of the drift, which is a super-critical quantity.

UR - http://www.scopus.com/inward/record.url?scp=84872942460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872942460&partnerID=8YFLogxK

U2 - 10.1007/s00205-012-0579-3

DO - 10.1007/s00205-012-0579-3

M3 - Article

AN - SCOPUS:84872942460

SN - 0003-9527

VL - 207

SP - 845

EP - 877

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -

On the Loss of Continuity for Super-Critical Drift-Diffusion Equations

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this