Navier-Stokesove jednadžbe

master's thesis

• Author: Filip Ivančić
• Mentor: Boris Muha (mentor)
• Committee member: Boris Muha (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Navier-Stokesove jednadžbe opisuju gibanje inkompresibilnog Newtonovog fluida. Unatoč detaljnom proučavanju kroz godine (problem je postavljen pred gotovo 200 godina), egzistencija i jedinstvenost glatkog rješenja i dalje su otvoreno pitanje i spadaju u jedan od milenijskih problema. Cilj ovog rada je pokazati egzistenciju i jedinstvenost slabog rješenja u dvije i tri dimenzije pod određenim uvjetima, diskutirati problematiku vezanu uz sama rješenja i konačno dati neke primjere primjena Navier-Stokesovih jednadžbi u realnim fizikalnim problemima.

Abstract (english)

Navier-Stokes equations describe motion of incompressible Newtonian fluid. Although heavily studied over the years (problem was set almost 200 years ago), it is still unsolved problem in classical sense - existence and uniqueness of smooth solutions - and is one of the millennium problems. Objective of this work is to show existence and uniqueness of weak solutions in two and three dimensions under certain conditions, discuss on the major problems, and give some examples of applications together with numerical simulations of real world problems.

• Keywords: inkompresibilan Newtonov fluid; glatko rješenje; slabo rješenje; Navier-Stokesove jednadžbe
• Keywords (english): incompressible Newtonian fluid; smooth solutions; weak solutions; Navier-Stokes equations
• Language: croatian
• URN:NBN: urn:nbn:hr:217:280073
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-30 13:04:46