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Stable Soliton Resolution for Wave M...

ProQuest Information and Learning Co.

Stable Soliton Resolution for Wave Maps on a Curved Spacetime.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Stable Soliton Resolution for Wave Maps on a Curved Spacetime./
Author:	Rodriguez, Casey Paul.
Description:	1 online resource (230 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355078046

Stable Soliton Resolution for Wave Maps on a Curved Spacetime.
Rodriguez, Casey Paul.

Stable Soliton Resolution for Wave Maps on a Curved Spacetime. - 1 online resource (230 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this thesis we study finite energy equivariant wave maps posed on the (1+3)--dimensional spherically symmetric static spacetime R x (R x S2) → S3 where the metric on R x (R x S2) is given by ds 2 = --dt2 + dr 2 + (r2 + 1) (dtheta 2 + sin2thetadϕ2), t,r ∈ R, (theta,ϕ) ∈ S 2. The metric is asymptotically flat with two ends at r = +/-infinity which are connected by a spherical ``throat" of area 4pi 2 at r = 0. The above spacetime is often cited as a simple example of a wormhole geometry in general relativity but is not expected to exist in nature due to the negative energy density required to obtain it.

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

Mode of access: World Wide Web

ISBN: 9780355078046Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Stable Soliton Resolution for Wave Maps on a Curved Spacetime.
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035 $a AAI10273455
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100 1 $a Rodriguez, Casey Paul. $3 1180714
245 1 0 $a Stable Soliton Resolution for Wave Maps on a Curved Spacetime.
264 0 $c 2017
300 $a 1 online resource (230 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: 78-12(E), Section: B.
500 $a Adviser: Carlos Kenig.
502 $a Thesis (Ph.D.) $c The University of Chicago $d 2017.
504 $a Includes bibliographical references
520 $a In this thesis we study finite energy equivariant wave maps posed on the (1+3)--dimensional spherically symmetric static spacetime R x (R x S2) → S3 where the metric on R x (R x S2) is given by ds 2 = --dt2 + dr 2 + (r2 + 1) (dtheta 2 + sin2thetadϕ2), t,r ∈ R, (theta,ϕ) ∈ S 2. The metric is asymptotically flat with two ends at r = +/-infinity which are connected by a spherical ``throat" of area 4pi 2 at r = 0. The above spacetime is often cited as a simple example of a wormhole geometry in general relativity but is not expected to exist in nature due to the negative energy density required to obtain it.
520 $a We consider equivariant wave maps from the previously described spacetime into the 3--sphere, S3. Each equivariant wave map can be indexed by its equivariance class l ∈ N and topological degree n ∈ N ∪ {0}. For each l and n, we prove that there exists a unique energy minimizing l-equivariant harmonic map Ql,n : R x (R x S2) → S3 of degree n. Based on mixed numerical and analytic evidence, Bizon and Kahl conjectured that all equivariant wave maps settle down to the harmonic map in the same equivariance and degree class by radiating off excess energy. In this thesis, we prove this conjecture rigorously and establish stable soliton resolution for this model; first for l = 1 (corotational maps) in Chapter 2, and then for general l > 1 in Chapter 3. More precisely, we show that modulo a free radiation term, every l-equivariant wave map of degree n converges strongly to Ql,n .
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 The University of Chicago. $b Mathematics. $3 1180611
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10273455 $z click for full text (PQDT)

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