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Incompressible Inhomogeneous Viscous Fluid Flows: Existence, Uniqueness and Regularity

He, Zihui 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)

Abstract (englisch):

This thesis is devoted to the study of the solvability and regularity problems for the motion of incompressible inhomogeneous viscous fluid flows in the presence of variable viscosity coefficients.

Chapter 2 is devoted to the existence and the regularity properties of (a class of) weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier-Stokes equations with density-dependent viscosity coefficients.
The three-dimensional case under special symmetry assumptions is also considered.

Chapter 3 proves the existence, uniqueness, and regularity results of the two-dimensional evolutionary incompressible Boussinesq equations with temperature-dependent thermal and viscosity diffusion coefficients in general Sobolev spaces.

In addition to the above results in the domain of fluid mechanics, we study the turbulence cascades for a two-parameter family of damped Szeg\H{o} equations in Chapter 4.


Volltext §
DOI: 10.5445/IR/1000144680
Veröffentlicht am 13.04.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Hochschulschrift
Publikationsdatum 13.04.2022
Sprache Englisch
Identifikator KITopen-ID: 1000144680
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 166 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Analysis (IANA)
Prüfungsdatum 06.04.2022
Schlagwörter Fluid mechanics, Navier-Stokes equations, Boussinesq equations, solvability, uniqueness, regularity, variable viscosity coefficient, variable thermal diffusivity, Sobolev spaces, Szegö equation, turbulence cascade
Referent/Betreuer Liao, Xian
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