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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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On fluids with pressure-dependent viscosity flowing through a porous medium
Žabenský, Josef ; Pokorný, Milan (advisor)
Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.
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Performance parameters measuring of combustion engines
Pokorný, Milan ; Pexa, Martin (advisor) ; Kotek, Tomáš (referee)
This thesis is focused on issues related to performance measurement of combustion engines. In the first chapter, these parameters are presented and discussed. Also shown here is a summary of the measurement methods used. The next two chapters these methods are divided. They mentioned their pros and cons, as well as devices that are used to implement them. In each of these chapters is described and evaluated its own measurements, which took place at the Department of quality and reliability of machines. The last chapter deals with describing some methods of measuring fuel consumption and a brief description of emission.
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