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Convex Integration and the Navier-Stokes Equations

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posted on 01.05.2020, 00:00 by Xiaoyutao Luo
This work is devoted to applying the convex integration technique that has been recently developed in fluid dynamics to the incompressible Navier-Stoke equations in dimensions $d \geq 3$. The main results include the existence of stationary weak solutions in dimensions $d \geq 4$ proved in Chapter 2 and in $3D$ which is proved in Chapter 3 where we also construct weak solutions in $3D$ whose energy profiles are discontinuous on some dense sets of positive Lebesgue measure in time.

History

Advisor

Cheskidov, Alexey

Chair

Cheskidov, Alexey

Department

Mathematics, Statistics and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Degree name

PhD, Doctor of Philosophy

Committee Member

Shvydkoy, Roman Sparber, Christof Dai, Mimi Silvestre, Luis

Submitted date

May 2020

Thesis type

application/pdf

Language

en

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