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Mechanisms of Lagrangian Analyticity...

Princeton University.

Mechanisms of Lagrangian Analyticity in Fluids.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Mechanisms of Lagrangian Analyticity in Fluids./
Author:	Hernandez, Matthew.
Description:	1 online resource (139 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355041828

Mechanisms of Lagrangian Analyticity in Fluids.
Hernandez, Matthew.

Mechanisms of Lagrangian Analyticity in Fluids. - 1 online resource (139 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Certain systems of inviscid fluid dynamics have the property that for solutions with just a modest amount of regularity in Eulerian variables, the corresponding Lagrangian trajectories are analytic in time. We elucidate the mechanisms in fluid dynamics systems that give rise to this automatic Lagrangian analyticity, as well as mechanisms in some particular fluids systems which prevent it from occurring.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355041828Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Mechanisms of Lagrangian Analyticity in Fluids.
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099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Hernandez, Matthew. $3 1180767
245 1 0 $a Mechanisms of Lagrangian Analyticity in Fluids.
264 0 $c 2017
300 $a 1 online resource (139 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: Charles L. Fefferman.
502 $a Thesis (Ph.D.) $c Princeton University $d 2017.
504 $a Includes bibliographical references
520 $a Certain systems of inviscid fluid dynamics have the property that for solutions with just a modest amount of regularity in Eulerian variables, the corresponding Lagrangian trajectories are analytic in time. We elucidate the mechanisms in fluid dynamics systems that give rise to this automatic Lagrangian analyticity, as well as mechanisms in some particular fluids systems which prevent it from occurring.
520 $a We give a conceptual argument for a general fluids model which shows that the fulfillment of a basic set of criteria results in the analyticity of the trajectory maps in time. We then apply this to the incompressible Euler equations, obtaining analyticity for vortex patch solutions in particular. We also use the method to prove the Lagrangian trajectories are analytic for solutions to the pressureless Euler-Poisson equations, for initial data with moderate regularity.
520 $a We then examine the compressible Euler equations, and find that the finite speed of propagation in the system is incompatible with the Lagrangian analyticity property. By taking advantage of this finite speed we are able to construct smooth initial data with the property that some corresponding Lagrangian trajectory is not analytic in time. We also study the Vlasov-Poisson system, uncovering another mechanism that damages the potential analytic properties of the trajectory map. In this instance, we find that a key nonlocal operator does not preserve analytic dependence in time. As a result, we can construct highly regular initial data with corresponding Lagrangian phase space flows that are not analytic as functions of time into the space of C 1 diffeomorphisms.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Princeton University. $b Mathematics. $3 1180706
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10285383 $z click for full text (PQDT)

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