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Regularity and Energy Laws in Hydrodynamic Models of Newtonian Fluids and Collective Behavior

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posted on 27.11.2018 by Trevor M. Leslie
We 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, Roman

Chair

Shvydkoy, Roman

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Bona, Jerry Cheskidov, Alexey Sparber, Christof Silvestre, Luis

Submitted date

August 2018

Issue date

12/06/2018

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