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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Stability of stationary flows of non-Newtonian heat conducting fluid in 2D
 Wintrová, Lucie ; Kaplický, Petr (advisor) ; Pokorný, Milan (referee)
This thesis aims to study the Navier-Stokes-Fourier problem with the entropy equa- tion. In particular, we want to define the notion of a solution and prove its existence. We approach this problem by modifying techniques used in several papers studying the generalized NSF system and the entropy equality and we want to conclude similar results. We are treating the two-dimensional case as opposed to the more frequent 3D case, hence we were able to relax conditions on the initial data. Firstly, we formulate the definition of a weak solution and impose sufficient conditions to prove its existence. In particular, we will require a bound p ≥ 2 for the power-law index of the Cauchy stress tensor. Next, we show that there exists a solution to Navier- Stokes-Fourier system (u, ϑ) fulfilling our definition. Lastly, we show that this solution additionally fulfills the entropy equality for η = log ϑ. 1
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Mathematical paradoxes
 Wintrová, Lucie ; Pick, Luboš (advisor) ; Zelený, Miroslav (referee)
In the presented bachelor thesis we will focus on mathematical paradoxes, especially the Banach-Tarski paradox. We will show several paradoxes concerning decompositions of sets, such as the Sierpiński-Mazurkiewicz paradox. Next, we perform a constructive proof of the Banach-Tarski theorem in R3 using a special group of rotations. Finally, we generalize the notion of equidecomposability to continuous equidecomposability and prove that the Banach-Tarski pardox holds even under the stricter condition of continuous equidecomposability. This will answer de Groot's question. 1
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