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Shape Optimization for Navier-Stokes Equations with Viscosity
Stebel, Jan ; Haslinger, Jaroslav (advisor) ; Feistauer, Miloslav (referee) ; Feireisl, Eduard (referee)
We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective is to analyze theoretically this problem (proof of the existence of a solution), its discretization and the numerical realization.
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Analysis of dissipative equations in unbounded domains
Michálek, Martin ; Pražák, Dalibor (advisor) ; Feireisl, Eduard (referee)
In the first part of this thesis, suitable function spaces for analysis of partial differ- ential equations in unbounded domains are introduced and studied. The results are then applied in the second part on semilinear wave equation in Rd with non- linear source term and nonlinear damping. The source term is supposed to be bounded by a polynomial function with a subcritical growth. The damping term is strictly monotone and satisfying a polynomial-like growth condition. Global existence is proved using finite speed of propagation. Dissipativity in locally uni- form spaces and the existence of a locally compact attractor are then obtained after additional conditions imposed on the damping term.
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Asymptotic Behavior of Solutions in Problems of the Mathematical Theory of Fluids
Kukučka, Peter ; Feireisl, Eduard (advisor) ; Málek, Josef (referee) ; Novotný, Antonín (referee)
This thesis contains a set of articles concerned with flow of a viscous, compressible and heat conducting fluids in several kinds of domains. The first part is devoted to the existence of weak solutions in domains that may contain cusps. Next chapter is focused on the asymptotic limit of the equations of magnetohydrodynamics consisting of Navier-Stokes-Fourier system describing the evolution of fluid coupled with Maxwell equations governing the behavior of magnetic field with the low Mach and Alfv'en number. At the end of the thesis, we study the asymptotic limit passage of the Navier-Stokes-Fourier system under the strong stratification defined in unbounded domain. Special attention is paid to the acoustic waves which analysis is based on local energy decay.
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Mathematical Analysis of Fluids in Large Domains
Poul, Lukáš ; Feireisl, Eduard (advisor) ; Pokorný, Milan (referee) ; Vodák, Rostislav (referee)
This thesis contains a set of articles concerned with flow of a viscous, compressible and heat conducting fluid in large domains. In the first part of the thesis, the existence of the weak solutions in unbounded domains is studied. The results follow each other in the way they were obtained through the time, and range from a simple extension to bounded domains with Lipschitz boundary up to the most general existence theorem for fluid flow in general open sets. The existence results are supplemented with the study of existence of weak solutions in the unbounded domain case with prescribed nonvanishing boundary conditions for density and temperature at infinity. The last contribution then concerns with the low Mach number limit in the compressible fluid flow.
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Mathematical analysis of fluids in motion
Michálek, Martin ; Feireisl, Eduard (advisor) ; Wiedemann, Emil (referee) ; Swierczewska - Gwiazda, Agnieszka (referee)
The aim of this work is to provide new results of global existence for dif- ferent evolution equations of fluid mechanics. We are in general interested in finding weak solutions without restrictions on the size of initial data. The proofs of existence are based on several different approaches including en- ergy methods, convergence analysis of finite numerical methods and convex integration. All these techniques significantly exploit results of mathematical analysis and other branches of mathematics. 1
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Compressible fluid motion in time dependent domains
Sýkora, Petr ; Feireisl, Eduard (advisor) ; Pokorný, Milan (referee)
In this work we study the existence of weak solutions for compressible Navier-Stokes equations in unbounded time dependent domains. Using the methods introduced in Feireisl E. Dynamics of Viscous Compressible Fluids we extend the results of article Feireisl E. Neustupa J. Stebel J., Convergence of a Brinkman-type penalization for compressible fluid flows, which studies the flow with a "no-slip" boundary condition on bounded domains. Next, we extend results of article Feireisl E. Kreml O. Nečasová Š. Neustupa J. Stebel J., Weak solutions to the barotropic Navier- Stokes system with slip boundary conditions in time dependent domains, which studies flow with compete Navier boundary condition. Finally, we discuss solutions for rotating fluid system. In this case, there are new members in momentum equation, representing the Coriolis and centrifugal force, which cause problems.
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