Global Regularity Aspects of Equations in Hydrodynamics

dc.contributor.committeeChairYamazaki, Kazuo
dc.contributor.committeeMemberBornia, Giorgio
dc.contributor.committeeMemberGelca, Razvan
dc.contributor.committeeMemberHoang, Luan
dc.creatorRahman, Mohammad Mahabubur
dc.date.accessioned2023-11-16T16:22:28Z
dc.date.available2023-11-16T16:22:28Z
dc.date.issued2023-08
dc.description.abstractThe question of the global regularity of the two-dimensional magnetohydrodynamics system without viscous dissipation is currently unknown. A challenging problem concerning the global regularity of the two-and-a-half and three-dimensional Hall-magnetohydrodynamics system is still open. The global regularity of two-dimensional and three-dimensional Kuramoto–Sivashinsky equations are not solved as well. Chapter 2 explores some cancellations and bounds within the Hall term for both two-and-a-half dimensional and three-dimensional cases, as well as various regularity criteria. The two-a-half-dimensional Hall equation and Hall-magnetohydrodynamics system are also proved to be globally well-posed when magnetic dissipation is considered at the below-critical level in the horizontal direction and at the supercritical level in the vertical direction. The purpose of Chapter 3 is to introduce and prove some global regularity criteria on the Sobolev and Besov spaces in dimensions two and three. In Chapter 4, a two-and-a-half-dimensional magnetohydrodynamics system is presented, and its global well-posedness is demonstrated. Furthermore, a magnetohydrodynamics system without viscous dissipation is introduced, and a global regularity criterion is derived.
dc.format.mimetypeApplication/pdf
dc.identifier.urihttps://hdl.handle.net/2346/96765
dc.language.isoen
dc.rights.availabilityAccess is not restricted.
dc.subjectNavier-Stokes equations
dc.subjectMagnetohydrodynamics system
dc.subjectHall-magnetohydrodynamics system
dc.subjectKuramoto-Sivashinsky equation
dc.subjectGlobal regularity,
dc.subjectGlobal regularity criteria
dc.titleGlobal Regularity Aspects of Equations in Hydrodynamics
dc.typeDissertation
thesis.degree.departmentMathematics and Statistics
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas Tech University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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