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This volume contains the proceedings of the International Conference on Vorticity, Rotation and Symmetry (IV)—Complex Fluids and the Issue of Regularity, held from May 8–12, 2017, in Luminy, Marseille, France. The papers cover topics in mathematical fluid mechanics ranging from the classical regularity issue for solutions of the 3D Navier-Stokes system to compressible and non-Newtonian fluids, MHD flows and mixtures of fluids. Topics of different kinds of solutions, boundary conditions, and interfaces are also discussed.
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
This thesis is devoted to the study of the basic equations of fluid dynamics. First Matthias Köhne focuses on the derivation of a class of boundary conditions, which is based on energy estimates, and, thus, leads to physically relevant conditions. The derived class thereby contains many prominent artificial boundary conditions, which have proved to be suitable for direct numerical simulations involving artificial boundaries. The second part is devoted to the development of a complete Lp-theory for the resulting initial boundary value problems in bounded smooth domains, i.e. the Navier-Stokes equations complemented by one of the derived energy preserving boundary conditions. Finally, the third part of this thesis focuses on the corresponding theory for bounded, non-smooth domains, where the boundary of the domain is allowed to contain a finite number of edges, provided the smooth components of the boundary that meet at such an edge are locally orthogonal.
Brennende Autos und eingeworfene Scheiben von Luxusimmobilien in Berlin, Demonstrationen und Hausbesetzungen in Paris: Die zunehmende sozialräumliche Spaltung der Bevölkerung entlädt sich immer häufiger in Protestaktionen. Der Begriff Gentrification hat dabei Eingang in gesellschaftliche Debatten gefunden und ist mittlerweile als "Reizthema" in den Fokus von Politik und Medien gerückt. Katharina Bröcker liefert einen wichtigen Beitrag zur deutsch-französischen Gentrificationforschung, indem sie die aktuell in Deutschland und Frankreich beobachtbaren Gentrificationprozesse am Beispiel des Bezirks Berlin-Prenzlauer Berg und den Pariser Vierteln Faubourg Saint-Antoine und Faubourg du Temple einander gegenüberstellt. Wie unterscheiden sich die spezifischen Ausprägungen der Gentrification in Form und Verlauf? Wie werden die Prozesse von der jeweiligen Gesellschaft wahrgenommen und welche politischen Maßnahmen zur Steuerung sind bekannt?
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