LESLIE-DISSERTATION-2018.pdf (1.33 MB)
Regularity and Energy Laws in Hydrodynamic Models of Newtonian Fluids and Collective Behavior
thesis
posted on 2018-11-27, 00:00 authored by Trevor M. LeslieWe consider several hydrodynamic models of Newtonian fluids and collective behavior, including the Euler and Navier-Stokes equations (both homogeneous and inhomogeneous) as well as the fractional Euler Alignment model. In each case we provide sufficient conditions to guarantee energy equality. We also give well-posedness results in large function spaces for the fractional Euler Alignment model, for which the existing well-posedness theory is less developed than for the other models we study.
History
Advisor
Shvydkoy, RomanChair
Shvydkoy, RomanDepartment
Mathematics, Statistics, and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral
Committee Member
Bona, Jerry Cheskidov, Alexey Sparber, Christof Silvestre, LuisSubmitted date
August 2018Issue date
2018-06-12Usage metrics
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