Online Archive of University of Virginia Scholarship
Several topics on the Navier-Stokes problem443 views
Author
Xu, Liaosha, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Advisors
Grujic, Zoran, Mathematics, University of Virginia
Abstract
Whether a 3D incompressible flow can spontaneously form a singularity, i.e. the global-in-time existence of the classical solution of the 3D Navier-Stokes equation, is still an open problem. This thesis provides several possible ways to explore regularity or criticality of the equation, with the notions of spatial intermittency and sparseness at scales as well as the harmonic analysis techniques regarding pointwise multipliers, singular integral operators, heat and Stokes semigroups in oscillation function spaces.
Degree
PHD (Doctor of Philosophy)
Keywords
Navier-Stokes equation, super-criticality, intermittency, sparseness at scales, turbulent flow, vortex stretching, space analyticity, asymmetry of singular profile, oscillatory intensity
Language
English
Rights
All rights reserved (no additional license for public reuse)
Xu, Liaosha. Several topics on the Navier-Stokes problem. University of Virginia, Mathematics - Graduate School of Arts and Sciences, PHD (Doctor of Philosophy), 2020-12-12, https://doi.org/10.18130/v3-fymc-kc28.
