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2D Peskin Problems of an Immersed El...
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Rodenberg, Analise.
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2D Peskin Problems of an Immersed Elastic Filament in Stokes Flow.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
2D Peskin Problems of an Immersed Elastic Filament in Stokes Flow./
作者:
Rodenberg, Analise.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2018,
面頁冊數:
152 p.
附註:
Source: Dissertation Abstracts International, Volume: 79-12(E), Section: B.
Contained By:
Dissertation Abstracts International79-12B(E).
標題:
Mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10824362
ISBN:
9780438168923
2D Peskin Problems of an Immersed Elastic Filament in Stokes Flow.
Rodenberg, Analise.
2D Peskin Problems of an Immersed Elastic Filament in Stokes Flow.
- Ann Arbor : ProQuest Dissertations & Theses, 2018 - 152 p.
Source: Dissertation Abstracts International, Volume: 79-12(E), Section: B.
Thesis (Ph.D.)--University of Minnesota, 2018.
In the work that follows we investigate a class of problems where a one dimensional closed elastic structure is immersed in a plane of steady Stokes flow. The dynamics are governed by a boundary integral equation describing the configuration of the immersed structure. Depending on the choice of elasticity law, we break our class into either a semilinear or fully nonlinear system of equations. In the nonlinear setting, we prove that the linearization of the system generates an analytic semigroup and use it to prove local existence and uniqueness in low regularity Holder spaces. In the semilinear setting, we remove the principle operator via small scale decomposition and use it to build similar local existence results. Further, we establish spatial smoothness of solutions by careful estimates on a class of commutators. Using these regularity results, we are able to establish that the only equilibria of the system are uniformly parameterized circles which we then prove nonlinear stability about. Finally, we identify a quantity which classifies global-in-time behavior.
ISBN: 9780438168923Subjects--Topical Terms:
515831
Mathematics.
2D Peskin Problems of an Immersed Elastic Filament in Stokes Flow.
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