Alongside the parabolic quasilinear method in fluid dynamics
Seiten
2015
Sierke Verlag
978-3-86844-737-8 (ISBN)
Sierke Verlag
978-3-86844-737-8 (ISBN)
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Parabolic quasilinear evolution equations naturally occur in mathematical fluid dynamics of complexly coupled fluid systems. One striking example are the Ericksen-Leslie equations modeling the dynamics of nematic liquid crystals – a material having both the characteristics of a fluid, namely a flow property, and also possessing structural properties of a crystal, namely a molecular orientational order.
In her thesis, Katharina Schade applies modern parabolic quasilinear theory to several systems related to the Ericksen-Leslie theory and arrives at a comprehensive understanding from the point of view of dynamical systems. These systems include the simplified Ericksen-Leslie equations (Lin-Liu 1995), thermodynamic and compressible extensions as well as a parameter-restricted version of the full Ericksen-Leslie equations.
In parabolic theory, understanding underlying linear problems is key for understanding non-linear systems. The author considers the notorious case of Lebesgue index p=∞ for the Lp-Stokes problem.
The question whether the Stokes operator generates an analytic semigroup in a space of essentially bounded solenoidal functions in cylindrical domains, is answered affirmatively using a de Giorgi-type contradiction argument.
In her thesis, Katharina Schade applies modern parabolic quasilinear theory to several systems related to the Ericksen-Leslie theory and arrives at a comprehensive understanding from the point of view of dynamical systems. These systems include the simplified Ericksen-Leslie equations (Lin-Liu 1995), thermodynamic and compressible extensions as well as a parameter-restricted version of the full Ericksen-Leslie equations.
In parabolic theory, understanding underlying linear problems is key for understanding non-linear systems. The author considers the notorious case of Lebesgue index p=∞ for the Lp-Stokes problem.
The question whether the Stokes operator generates an analytic semigroup in a space of essentially bounded solenoidal functions in cylindrical domains, is answered affirmatively using a de Giorgi-type contradiction argument.
Erscheinungsdatum | 13.09.2017 |
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Verlagsort | Göttingen |
Sprache | englisch |
Einbandart | geklebt |
Themenwelt | Mathematik / Informatik ► Mathematik |
Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
Schlagworte | Ericksen-Leslie Theorie • Mathematische Fluid Dynamik • Maximaleregularität • Navier-Stokes Gleichungen • Nematische Flüssigkristalle • Parabolische Probleme • Quasilineare Probleme • Stokes Gleichung |
ISBN-10 | 3-86844-737-7 / 3868447377 |
ISBN-13 | 978-3-86844-737-8 / 9783868447378 |
Zustand | Neuware |
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