Data assimilation in the theory of non-Newtonian fluids
| Thesis title in Czech: | Asimilace dat v teorii nenewtonskych tekutin |
|---|---|
| Thesis title in English: | Data assimilation in the theory of non-Newtonian fluids |
| Key words: | neNewtonské tekuitny|asimilace dat|existence slabého řešení|jednoznačnost|dlouhodobé chování |
| English key words: | non-Newtonian fluids|data assimilation|existence of weak solution|uniqueness|long-time behaviour |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | doc. RNDr. Miroslav Bulíček, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 26.02.2022 |
| Date of assignment: | 28.02.2022 |
| Confirmed by Study dept. on: | 04.03.2022 |
| Date and time of defence: | 06.06.2023 09:00 |
| Date of electronic submission: | 26.04.2023 |
| Date of submission of printed version: | 09.05.2023 |
| Date of proceeded defence: | 06.06.2023 |
| Opponents: | RNDr. Václav Mácha, Ph.D. |
| Advisors: | doc. Mgr. Petr Kaplický, Ph.D. |
| Guidelines |
| 1) Student se seznámí se základní teorií o existenci a jednoznačnosti slabých řešení pro zobecněné Navierovy-Stokesovy rovnice.
2) Student se seznámí se základními poznatky o asimilaci dat v teorii evolučních PDR. 3) Získané poznatky student aplikuje na problémy teorie proudění pro nenewtonovské tekutiny ve dvou a třídimenzionálním proudění. |
| References |
| Yu Cao, Andrea Giorgini, Michael Jolly and Ali Pakzad: Continuous Data Assimilation For the 3D Ladyzhenskaya Model: Analysis and Computations, arXiv: 2108.03513, 2021
Abderrahim Azouani, Eric Olson, and Edriss S. Titi: Continuous data assimilation using general interpolant observables. J. Nonlinear Sci. 24 (2014), no. 2, 277–304. Animikh Biswas and Randy Price: Continuous data assimilation for the three-dimensional Navier-Stokes equations, SIAM J. Math. Anal. 53 (2021), no. 6, 6697–6723. Miroslav Bulíček, Petr Kaplický and Dalibor Pražák: Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth, Math. Models Methods Appl. Sci., 29, No. 6, 1207--1225, 2019 |