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Data assimilation in the theory of non-Newtonian fluids
Mosný, Stanislav ; Bulíček, Miroslav (advisor) ; Mácha, Václav (referee)
The purpose of this thesis is to provide a detailed proof of the well-posedness of the Ladyzhenskaya model and to study the data assimilation problem for this model. The thesis is divided into three parts. In the first part we study the Ladyzhenskaya model in two dimensions. This part serves as a general introduction into modern PDE theory, and the methods used here can be applied to a wider range of problems. We define the notion of weak solution, show uniform estimates for the finite dimensional approximations of the weak solution and prove it's existence via weak-compactness method. We also show uniqueness of weak solution. The second part is devoted to the data assimilation of the Ladyzhenskaya model in two dimensions. We show that the assimilation problem posses a weak solution and we study the convergence to the reference solution. We derive the bounds for the relaxation parameter and the spacial resolution of measured data, based on the long-time behaviour of the original problem. In the third and final part we study the data assimilation for the Ladyzhenskaya model in three dimensions. We establish well-posedness for p ≥ 5/2. We modify bounds for the behaviour of a solution when time approaches infinity and derive conditions for the data assimilation parameters, under which the assimilated solution...
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Existence and Qualitative Properties of Solutions to Certain Systems of Fluid Mechanics
Mácha, Václav
anglicky In the presented work, we study the existence and uniqueness of solutions to the generalized Stokes problem. We, further, focus on the higher differentiability and the Hölder continuity of solutions to the generalized Stokes and generalized Navier-Stokes system. We reach the full regularity in an arbitrary dimension for a linear case, while in a nonlinear case we work only in dimensions d = 2, 3. In dimension d = 2 we are able to proof the full regularity of solution, in dimension d = 3 we obtain only a partial regularity. All main results are introduced in the first section. 1
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Existence and Qualitative Properties of Solutions to Certain Systems of Fluid Mechanics
Mácha, Václav ; Stará, Jana (advisor) ; Pražák, Dalibor (referee) ; Skalák, Zdeněk (referee)
anglicky In the presented work, we study the existence and uniqueness of solutions to the generalized Stokes problem. We, further, focus on the higher differentiability and the Hölder continuity of solutions to the generalized Stokes and generalized Navier-Stokes system. We reach the full regularity in an arbitrary dimension for a linear case, while in a nonlinear case we work only in dimensions d = 2, 3. In dimension d = 2 we are able to proof the full regularity of solution, in dimension d = 3 we obtain only a partial regularity. All main results are introduced in the first section. 1
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Existence and Qualitative Properties of Solutions to Certain Systems of Fluid Mechanics
Mácha, Václav
anglicky In the presented work, we study the existence and uniqueness of solutions to the generalized Stokes problem. We, further, focus on the higher differentiability and the Hölder continuity of solutions to the generalized Stokes and generalized Navier-Stokes system. We reach the full regularity in an arbitrary dimension for a linear case, while in a nonlinear case we work only in dimensions d = 2, 3. In dimension d = 2 we are able to proof the full regularity of solution, in dimension d = 3 we obtain only a partial regularity. All main results are introduced in the first section. 1
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Application of Fredholm's theorems to the existnce of solutions to systems of Stokes type
Mácha, Václav ; Stará, Jana (advisor) ; Kaplický, Petr (referee)
Presented work deals with the existence and uniqueness of solution of generalized Stokes problem. The study of this problem is motivated by the research concerning partial regularity of weak solutions of systems describing the flow of incompressible fluids whose viscosity depends on the pressure and the shear rate. The explanation of the connection between presented problems is desribed in the first chapter, which includes also some models of viscosity. In following chapters the existence and uniqueness of solutions are studied with regard to the changing parametrs in models of viscosity. For this purpose I use compact embeddings followed by appropriate application of Fredholms theorems. At the end of the work the constructed theory is applied to one viscosity model.
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Computer modelling in programming language COMSOL Multiphysics
MÁCHA, Václav
The thesis deals with a computer modelling by means of the commercial software COMSOL Multiphysics. The thesis is structured into three topical sections. The first part is dedicated to the programme characteristics and its development. In the second part the brief characteristics of working with the programme COMSOL Multiphysics is presented which should make the user´s first steps in working with software easier. The last part of thesis shows the specific demonstration of the created multiple physics task taken from the field of plasma physics. This task is solved by means of continuous simulation of a computer modelling based on the drift-diffusion approximation of low temperature plasma. The proposal of the paper for the proceedings of the conference ,,Technical Computing Prague 2012" is also a part of this thesis.
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