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Interface Problems in Two-Phase Magnetohydrodynamic Flows

Jing, Tian (2023) Interface Problems in Two-Phase Magnetohydrodynamic Flows. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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We study the motion of two incompressible, conductive fluids in a magnetic field. The viscosity and surface tension are considered. The study includes the existence of varifold solutions, strong solutions, and their weak-strong uniqueness. To obtain varifold solutions, we approximate the equations using the Galerkin method. Using solution operators and the Schauder fixed-point theorem, we can obtain the approximate solutions. The weak convergence method is then used for studying the limit of approximate solutions. Varifolds are used for describing the interface. To find a strong solution, we apply the Hanzawa transformation to the equations, which are transformed into a fixed-interface problem for a short time. The new equations are divided into principal parts and nonlinear parts, which are studied separately. The solution is obtained using the fixed point theory of contraction mappings. When the strong solution exists, all varifold solutions coincide with it. This is proved by estimating the error between strong and varifold solutions using the relative entropy. An inequality of the relative entropy is derived and controlled by utilizing the Gronwall’s inequality.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Jing, Tiantij11@pitt.edutij110000-0002-9283-4242
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairWang,
Committee MemberSchikorra,
Committee MemberChen,
Committee MemberTice,
Date: 11 May 2023
Date Type: Publication
Defense Date: 16 March 2023
Approval Date: 11 May 2023
Submission Date: 3 April 2023
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 145
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: 3-D MHD, two-phase, varifold solutions, strong solutions, weak-strong uniqueness.
Date Deposited: 11 May 2023 13:02
Last Modified: 11 May 2023 13:02


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