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On the Mixing of Incompressible Flow...
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ProQuest Information and Learning Co.
On the Mixing of Incompressible Flows and on The Geometry of Regularized Optimal Transport.
Record Type:
Language materials, manuscript : Monograph/item
Title/Author:
On the Mixing of Incompressible Flows and on The Geometry of Regularized Optimal Transport./
Author:
Leger, Flavien.
Description:
1 online resource (74 pages)
Notes:
Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Contained By:
Dissertation Abstracts International79-04B(E).
Subject:
Mathematics. -
Online resource:
click for full text (PQDT)
ISBN:
9780355407020
On the Mixing of Incompressible Flows and on The Geometry of Regularized Optimal Transport.
Leger, Flavien.
On the Mixing of Incompressible Flows and on The Geometry of Regularized Optimal Transport.
- 1 online resource (74 pages)
Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Thesis (Ph.D.)
Includes bibliographical references
In the first part of this thesis we consider mixing by incompressible flows. In 2003, Bressan stated a conjecture concerning a bound on the mixing achieved by the flow in terms of an L1 norm of the velocity field. Existing results in the literature use an Lp norm with p > 1. We introduce a new approach to prove such results. It recovers most of the existing results and offers new perspective on the problem. Our approach makes use of a recent harmonic analysis estimate from Seeger, Smart and Street.
Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018
Mode of access: World Wide Web
ISBN: 9780355407020Subjects--Topical Terms:
527692
Mathematics.
Index Terms--Genre/Form:
554714
Electronic books.
On the Mixing of Incompressible Flows and on The Geometry of Regularized Optimal Transport.
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Leger, Flavien.
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On the Mixing of Incompressible Flows and on The Geometry of Regularized Optimal Transport.
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Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
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Advisers: Nader Masmoudi; Alfred Galichon.
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Thesis (Ph.D.)
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New York University
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2017.
504
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Includes bibliographical references
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In the first part of this thesis we consider mixing by incompressible flows. In 2003, Bressan stated a conjecture concerning a bound on the mixing achieved by the flow in terms of an L1 norm of the velocity field. Existing results in the literature use an Lp norm with p > 1. We introduce a new approach to prove such results. It recovers most of the existing results and offers new perspective on the problem. Our approach makes use of a recent harmonic analysis estimate from Seeger, Smart and Street.
520
$a
In the second part of the thesis we present new geometric intuition on dynamical versions of regularized optimal transport. We introduce two families of variational problems on Riemannian manifolds which contain analogues of the Schrodinger bridge problem and the Yasue problem. We also propose an analogue of the Hopf-Cole transformation in the geometric setting.
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Ann Arbor, Mich. :
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ProQuest,
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2018
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Mode of access: World Wide Web
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Mathematics.
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ProQuest Information and Learning Co.
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New York University.
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Dissertation Abstracts International
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79-04B(E).
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http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10287505
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click for full text (PQDT)
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