On the existence of solutions to the Muskat problem with surface tension / Spencer Tofts.

Format:

Book

Manuscript

Thesis/Dissertation

Author/Creator:

Tofts, Spencer, author.

Contributor:

Strain, Robert, degree supervisor, degree committee member.

Croke, Christopher, 1985- degree committee member.

Gressman, Philip, degree committee member.

University of Pennsylvania. Department of Mathematics, degree granting institution.

Language:

English

Subjects (All):

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Physical Description:

v, 118 leaves ; 29 cm

Production:

[Philadelphia, Pennsylvania] : University of Pennsylvania, 2016.

Summary:

We consider the Muskat Problem with surface tension in two dimensions over the real line, with Hs initial data and allowing the two fluids to have different constant densities and viscosities. We take the angle between the interface and the horizontal, and derive an evolution equation for it. We use energy methods to prove that a solution [theta] exists locally and can be continued while ||[theta]||s remains bounded and the arc chord condition holds. Furthermore, the resulting solution is unique, and depends continuously on the initial data. Additionally, when both fluids have the same viscosity and the initial data is sufficiently small, we show the energy is non-increasing, and that the solution [theta] exists globally in time.

Notes:

Ph. D. University of Pennsylvania 2016.

Department: Mathematics.

Supervisor: Robert Strain.

Includes bibliographical references.

OCLC:

960100886