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master's thesis
Dinamika Navier-Stokesove jednadžbe
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:119947
Martinčić, Tijana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Martinčić, T. (2021). Dinamika Navier-Stokesove jednadžbe (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:119947

Martinčić, Tijana. "Dinamika Navier-Stokesove jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:119947

Martinčić, Tijana. "Dinamika Navier-Stokesove jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:119947

Martinčić, T. (2021). 'Dinamika Navier-Stokesove jednadžbe', Master's thesis, University of Zagreb, Faculty of Science, accessed 06 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:119947

Martinčić T. Dinamika Navier-Stokesove jednadžbe [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 December 06] Available at: https://urn.nsk.hr/urn:nbn:hr:217:119947

T. Martinčić, "Dinamika Navier-Stokesove jednadžbe", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:119947

Metadata
TitleDinamika Navier-Stokesove jednadžbe
Title (english)Dynamics of the Navier-Stokes equation
AuthorTijana Martinčić
MentorSiniša Slijepčević (mentor)
Committee memberSiniša Slijepčević (predsjednik povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberMarko Radulović (član povjerenstva)
Committee memberGoran Igaly (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu izveli smo Navier-Stokesove jednadžbe. Navier-Stokesove jednadžbe opisuju gibanje inkompresibilnog, homogenog, Newtonovskog fluida. Unatoč rasprostranjenosti primjene, egzistencija i jedinstvenost rješenja i dalje nisu potpuno dokazani. U prvom poglavlju uveli smo funkcijske prostore ključne za teorijsko proučavanje problema. To su prostori glatkih funkcija, Lebesgueovi i Soboljevi prostori. Drugo poglavlje posvećeno je uvodenju rubnih i početnih uvjeta kako bi imali potpuno postavljen problem. Zbog kompleksnosti Navier-Stokesovih jednadžbi nemamo globalnu egzistenciju i jedinstvenost rješenja. Zato se treće poglavlje bavi izvođenjem slabe formulacije problema. I za kraj, zadnje poglavlje daje nam rezultate o egzistenciji i jedninstvenosti slabog i jakog rješenja u dimenzijama 2 i 3.
Abstract (english)
In this diploma thesis we derived Navier-Stokes equations. Navier-Stokes equations describe the motion of an incompressible, homogeneous, Newtonian fluid. Despite the prevalence of application, the existence and uniqueness of the solution are still not fully proven. In the first chapter we introduced functional spaces that are fundamental for the theoretical study of the problem. These are spaces of smooth functions, Lebesque spaces and Sobolev spaces. The second chapter is focused to the introduction of boundary and initial conditions in order to have a fully posed problem. Due to the complexity of Navier-Stokes equations, we do not have the global existence and uniqueness of the solution. Therefore, the third chapter deals with deriving a weak formulation of the problem. Finally, the last chapter gives us results on the existence and uniqueness of a weak and strong solution in dimensions 2 and 3.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:119947
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-10-29 11:16:08