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Generalized Stokes systems - theoretical analysis approach
Holeček, Martin ; Pokorný, Milan (referee) ; Málek, Josef (advisor)
We consider steady flows of homogenous incompressible fluid described by generalized Stokes system. We study two models, first with shear-rate dependent viskosity and second with pressure and shear-rate dependent viskosity. We investigate internal flows in bounded domains subject to Navier's boundary condition. First, to show the difference, we present proofs of existence and uniqueness of solutions for both systems. Then we investigate, what are the assumptions allowing to take the fluid mechanics limit, as Navier's boundary conditions approximate first no-slip and then (perfect) slip boundary conditions. Finally, we consider for simplicity specially periodic problem and show regularity result (integrability of the second derivatives of the velocity and the first derivatives of the pressure).
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How to interpret Kafka? Criticism of the Czech reception of Kafka's work and an attempt a new approach
Soukup, Jiří ; Bílek, Petr (referee) ; Pokorný, Martin (advisor)
The point of departure of this thesis is a detailed research into Kafka's early periodical publications and into the earliest German reception connected to them. The Czech reception, not following until the first Kafka's book, is investigated here in several steps: desribed is as whole the Czech reception during Kafka's lifetime (1913-1923), at large the period before the February Coup d'état (1924-1948) and in a summarizing chapter we focus on the history of Kafka's reception until these days (1948-2010). The typological part of this thesis analyzes then in detail two different philosophical approaches to Kafka: the unsatisfactory Calasso's conception and an original understanding by Matěj Král. The aim is to distinguish productive lines of Kafka's philosophical interpretations through a substantial analysis and critique.
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Existenční teorie pro velká data pro nestacionární proudění vazkopružných tekutin
Pušman, Jan ; Málek, Josef (advisor) ; Pokorný, Milan (referee)
In the present. work, we investiga te some evolutionary viscoelastic fluid models of Oldroyd type. The model consis of the incompressible Navier-Stokes equations coupled with transport equations for components of stress tensor. We provide a more detailed proof of the exis tence of weak solutions in case of space periodic boundary conditions following the original paper by Lion s and Masrnoudi. The proof is based on exploiting the propagation in time of the compactness of the solutions, i.e. the property that if we take a sequence of weak solution s which converges weakly and such that the corresponding initial conditions converge strongly, then the weak limit is also a solution.
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Regularity of solutions of systems describing generalized Newtonian fluids
Tichý, Jakub ; Kaplický, Petr (advisor) ; Pokorný, Milan (referee)
We investigate properties of solutions of systems of nonlinear partial differential equations describing evolutionary flow of certain class of generalized Newtonian fluids including in particular various variants of the power-law models. We study the problem with perfect slip boundary conditions. The nonlinear elliptic operator, which is related to the stress tensor, has a p-potential structure. We focus especially on the case p = 2. The main part of the work deals with regularity of second space derivatives and overcoming new di±culties connected with usage of considered boundary conditions.
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Fourier method for solving partial differential equations
Tůma, Karel ; Knobloch, Petr (referee) ; Pokorný, Milan (advisor)
Na./cv prace: Fouricrova metoda pro feseni parc.ialnich dirornncialnich rovnic Autor: Karri Tuma Katedra (ust.av): Matematicky ust.av UK Vedouci bakalafske praoo: Mgr. Milan Pokorny, Ph.D. e-mail vodouciho: pokorny@karlin.mff.cuni.cz Abstra.kt: V pfedlo/ene praci odvodime rovnici vedeni tepla a.rovnici slruny. Ty pak nasledno. fesime v jodno prost.orove dimenxi ponioci Fonricrovy me- tody apocivajfci v separaci promennych a nale/eni feseni vc l.varn ncko- nccnc' fady. Zaljyvainc so t.fonii ru/nymi okrajovynii podininkanii. Dah^ vy- sotrujomo vlastnosii foscni tcchlo dvou problcmu. Provadinio analyzu kon- vorgtuicc fx'soni vu tvaru fad v -/avislosti na pocat.ocnich podminkach uloh. Uka/c-me. /o pornoci Fouriorovy inolody l/.c fosil lako stucionarni ulohy, konkrctno so zabyvanio Laplaccoviju rovnici s okrajovynii podminkami na ruznych oblasloch (kruh. vyscc. vyscc mc/ikru/f, mraikru/i). Klicova slova: Parcialni diforoncialni rovnico, Fouricrova tnot.oda, rovnico vodoni lopla, rovnico sLruny. Title: Fourier method for solving partial differential equations Author: Karel Tuma, Department: Matematicky ustav UK Supervisor: Mgr. Milan Pokorny. Ph.D. Supervisor's e-mail address: pokorny@karlin.raff.cuni.cz Abstract: In the present work we derive the heat equation and the wave equation. They arc- solved in one space...
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