Compressible Navier-Stokes-Fourier system for the adiabatic coefficient close to one
| Thesis title in Czech: | Stlačitelné Navier-Stokes-Fourierovy rovnice pro adiabatický koeficient blízko jedničky |
|---|---|
| Thesis title in English: | Compressible Navier-Stokes-Fourier system for the adiabatic coefficient close to one |
| Key words: | stlačitelné Navier-Stokes-Fourierovy rovnice; slabé řešení; dvoudimenzionální proudění; Orliczovy prostory |
| English key words: | compressible Navier-Stokes-Fourier system; weak solution; two dimensional flow; Orlicz spaces |
| Academic year of topic announcement: | 2018/2019 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| 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: | 11.10.2018 |
| Date of assignment: | 12.10.2018 |
| Confirmed by Study dept. on: | 18.10.2018 |
| Date and time of defence: | 12.09.2019 08:00 |
| Date of electronic submission: | 19.07.2019 |
| Date of submission of printed version: | 19.07.2019 |
| Date of proceeded defence: | 12.09.2019 |
| Opponents: | prof. RNDr. Eduard Feireisl, DrSc. |
| Guidelines |
| The aim of the thesis is to prove existence of a weak solution for the evolutionary compressible Navier-Stokes-Fourier system in two space dimensions in the case when the cold pressure behaves like "\rho \ln^\alpha (1+\rho)" for some \alpha positive, without any assumptions on the size of the data. In this case the density is typically estimated in some Orlicz spaces. The thesis will also contain the construction of the weak solution. |
| References |
| Erban, Radek: On the existence of solutions to the Navier-Stokes equations of a two-dimensional compressible flow. Math. Methods Appl. Sci. 26 (2003), no. 6, 489–517.
Feireisl, Eduard; Novotný, Antonín: Singular limits in thermodynamics of viscous fluids. Second edition. Advances in Mathematical Fluid Mechanics. Birkhäuser/Springer, Cham, 2017. Pokorný, Milan: On the steady solutions to a model of compressible heat conducting fluid in two space dimensions. J. Partial Differ. Equ. 24 (2011), no. 4, 334–350. |