Stacionární stlačitelné Navier-Stokes-Fourierovy rovnice
| Thesis title in Czech: | Stacionární stlačitelné Navier-Stokes-Fourierovy rovnice |
|---|---|
| Thesis title in English: | Steady compressible Navier-Stokes-Fourier equations |
| Key words: | slabé řešení; entropická nerovnost; vnější oblasti; silné řešení; prostorová asymptotika; oblasti s nekompaktní hranicí |
| English key words: | weak solution; entropy inequality; exterior domain; strong solution; spatial asymptotics; domains with non-compact boundaries |
| Academic year of topic announcement: | 2019/2020 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | prof. Mgr. Milan Pokorný, Ph.D., DSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 29.08.2019 |
| Date of assignment: | 29.08.2019 |
| Confirmed by Study dept. on: | 02.10.2019 |
| Advisors: | Mgr. Ondřej Kreml, Ph.D. |
| Guidelines |
| The aim of the doctoral thesis is the study of the steady equations describing the flow of compressible heat-conducting Newtonian fluid in different situations. The first part deals with the existence of weak solutions in situations when the viscosity behaves like (1+ θ)a, where θ is the temperature and the exponent a is different from 1. Next, existence of weak solutions in unbounded domain, in particular in domains with non-compact boundaries will be considered.
Second part of the thesis will deal with classical solutions and in particular with existence of solutions in exterior domain, where also the decay of solutions at infinity will be studied. |
| References |
| [1] Mucha, Piotr B., Pokorny, Milan, Zatorska, Ewelina: Existence of Stationary Weak Solutions for the Heat Conducting Flows. In: Giga, Yoshikazu, Novotn\'y, Anton\'\i n (eds.): Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Springer Verlag, 2018, 2595-2662.
[2] Novo, Sebastian, Novotny, Antonin, Pokorny, Milan: Steady compressible Navier-Stokes equations in domains with non-compact boundaries, Mathematical Methods in the Applied Sciences 28 (2005), 1445-1479. [3] Pokorny, Milan: Asymptotic behaviour of solutions to certain partial differential equations describing the flow of fluids in unbounded domains. PhD. Thesis, University of Toulon and Charles University, Prague, 1999. [4] Dutto, Patrick, Novotny, Antonin: Physically Reasonable Solutions to Steady Compressible Navier-Stokes Equations in 2d Exterior Domains with Nonzero Velocity at Infinity, Journal of Mathematical Fluid Mechanics 3 (2001), 99-138. |