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Almost well-posedness of the full water wave equation on the finite stripe domain

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dc.contributor.authorZhu, Benbenen
dc.contributor.committeechairSun, Shu Mingen
dc.contributor.committeememberYue, Pengtaoen
dc.contributor.committeememberLiu, Honghuen
dc.contributor.committeememberLin, Taoen
dc.contributor.departmentMathematicsen
dc.date.accessioned2023-08-19T08:00:31Zen
dc.date.available2023-08-19T08:00:31Zen
dc.date.issued2023-08-18en
dc.description.abstractThe dissertation gives a rigorous study of surface waves on water of finite depth subjected to gravitational force. As for `water', it is an inviscid and incompressible fluid of constant density and the flow is irrotational. The fluid is bounded above by a free surface separating the fluid from the air above (assumed to be a vacuum) and below by a rigid flat bottom. Then, the governing equations for the motion of the fluid flow are called Euler equations. If the initial fluid flow is prescribed at time zero, i.e., mathematically the initial condition for the Euler equations is given, the long-time existence of a unique solution for the Euler equations is still an open problem, even if the initial condition is small (or initial flow is almost motionless). The dissertation tries to make some progress for proving the long-time existence and show that the time interval of the existence is exponentially long, called almost global well-posedness, if the initial condition is small and satisfies some conditions. The main ideas for the study are from the corresponding almost global well-posedness result for surface waves on water of infinite depth.en
dc.description.abstractgeneralThis dissertation concerns the mathematical study of surface waves on water of finite depth under gravitational force. Mathematically, water is considered as a fluid of constant density that has no viscosity and is incompressible. It is also assumed that any portion of the corresponding fluid flow is not rotating. Furthermore, the water is bounded above by a free surface separating the water from the air above and below by a rigid horizontal flat bottom. A natural question to ask is whether the water surface will keep smooth and will not break as time progresses, if a small disturbance on the flat free surface and the tranquil water-body is initially created. The dissertation tries to make some progress on this question by showing that under some mathematical and technical assumptions, the water surface remains smooth and will not break for a very long time by using the mathematical equations derived from the laws of physics.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:38435en
dc.identifier.urihttp://hdl.handle.net/10919/116062en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectsurface wavesen
dc.subjectfinite depthen
dc.subjectlong-time existenceen
dc.subjectunique solutionen
dc.subjectalmost global well-posednessen
dc.titleAlmost well-posedness of the full water wave equation on the finite stripe domainen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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