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VORTEX SHEETS IN ELASTIC FLUIDS

Hu, Jilong (2017) VORTEX SHEETS IN ELASTIC FLUIDS. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

The stability and existence of compressible vortex sheets is studied for two-dimensional isentropic elastic flows. This problem has a free boundary with extra difficulties that the boundary is characteristic and the Kreiss-Lopatinskii condition holds only in a weak sense. A necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets. More precisely, it is shown that, besides the stable supersonic zone, the elasticity exerts an additional stable subsonic zone. Moreover we also obtain the linear stability of the variable states and the local in time existence of the vortex sheets near the stable rectilinear vortex sheets.

For the linear stability, we employ the Fourier transform and para-differential calculus to perform the spectrum analysis. Since only the weak Kreiss-Lopatinskii condition holds, the a priori estimates for the linearized system exhibit the loss of derivatives. Thus the existence of vortex sheets is proved by a suitable variation of Nash-Moser iteration scheme.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Hu, Jilongjih62@pitt.edujih62
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairWang, Dehuadhwang@pitt.edu
Committee MemberChen, Mingmingchen@pitt.edu
Committee MemberJiang, Huiqianghqjiang@pitt.edu
Committee MemberTice, Ianiantice@andrew.cmu.edu
Date: 26 June 2017
Date Type: Publication
Defense Date: 6 January 2017
Approval Date: 26 June 2017
Submission Date: 3 May 2017
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 159
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Vortex sheets, Elastodynamics, Contact discontinuities, Linear stability, Loss of derivatives, Para-differential calculus, Nash-Moser iteration
Date Deposited: 26 Jun 2017 13:02
Last Modified: 26 Jun 2017 13:02
URI: http://d-scholarship.pitt.edu/id/eprint/31682

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