Journal article icon

Journal article

Parabolic equations with singular divergence‐free drift vector fields

Abstract:

In this paper, we study an elliptic operator in divergence form but not necessarily symmetric. In particular, our results can be applied to elliptic operator L=νΔ+u(x,t)·∇, where u(·,t) is a time‐dependent vector field in ℝn, which is divergence‐free in the distributional sense, that is ∇·u=0. Suppose u∈L∞(0,∞;BMO−1(ℝn)). We show the existence of the fundamental solution Γ(x,t;ξ,τ) of the parabolic operator L−∂t and show that Γ satisfies the Aronson estimate with a constant depending only on ...

Expand abstract
Publication status:
Published
Peer review status:
Peer reviewed

Actions


Access Document


Files:
Publisher copy:
10.1112/jlms.12202

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Exeter College
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
More from this funder
Name:
Engineering and Physical Sciences Research Council
Funding agency for:
Xi, G
Grant:
EP/L015811/1
More from this funder
Name:
European Research Council
Funding agency for:
Qian, Z
Grant:
Esig ID 291244
Publisher:
London Mathematical Society
Journal:
Journal of the London Mathematical Society More from this journal
Volume:
100
Issue:
1
Pages:
17-40
Publication date:
2018-12-06
Acceptance date:
2018-11-20
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Keywords:
Pubs id:
pubs:944246
UUID:
uuid:282d650c-28d2-44af-8c69-81ffcae39626
Local pid:
pubs:944246
Source identifiers:
944246
Deposit date:
2018-11-20

Terms of use


Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP