Partial regularity results for the three-dimensional incompressible Navier-Stokes equation

dc.contributor.advisorCaffarelli, Luis A.
dc.contributor.advisorVasseur, Alexis F.
dc.contributor.committeeMemberVicol, Vlad C
dc.contributor.committeeMemberVishik, Mikhail M
dc.creatorYang, Jincheng, Ph. D.
dc.creator.orcid0000-0002-3581-9425
dc.date.accessioned2023-04-27T00:43:22Z
dc.date.available2023-04-27T00:43:22Z
dc.date.created2022-05
dc.date.issued2022-04-01
dc.date.submittedMay 2022
dc.date.updated2023-04-27T00:43:23Z
dc.description.abstractWe show a series of works of some regularity results on the incompressible Navier-Stokes equation in dimension three. Using the blow-up method, we estimate the higher regularity in the Lorentz norm for smooth solutions to the Navier-Stokes equation. In particular, we show a second derivative estimate for suitable weak solutions, which improves the currently known regularity. We construct a maximal function associated with geometric objects that we call skewed cylinders, appearing in inviscid flows like the Eulerian cylinders around the Lagrangian trajectories. We also apply the blow-up method to estimate the boundary vorticity, which enables us to achieve an unconditional control of the layer separation of Leray-Hopf solutions from a steady shear flow in a finite periodic channel.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2152/118415
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/45294
dc.language.isoen
dc.subjectNavier-Stokes equation
dc.subjectPartial regularity
dc.subjectMaximal function
dc.subjectInviscid limit
dc.subjectBlow-up technique
dc.titlePartial regularity results for the three-dimensional incompressible Navier-Stokes equation
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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