Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Γεράσιμος Μπαρμπάτης ,Καθηγητής ,Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο
Original Title:
Η Εξίσωση Navier- Stokes στις τρείς διαστάσεις
Translated title:
The Navier- Stokes Equation in three dimensions
Summary:
In this master thesis we will study the Navier - Stokes equation in three
dimensions , which is a fundamental partial differential equation for fluid
dynamics with several applications to real life problems , but it is still an
open problem.
In the first Chapter we introduce some initial concepts mostly from
functional analysis such as Lebesgue, Sobolev and Bochner spaces .We will
also mention some important theorems and properties for these spaces in
order to use them in the next chapters.
In Chapter 2 we will discuss important tools for the study of the Navier -
Stokes equation such as the Helmholtz - Weyl decomposition and the Stokes
operator.
Later , in Chapter 3 we will present the construction of weak solutions in
two different spaces of test functions and some properties. Furthermore we
will refer to the uniqueness of weak solutions for the two dimensional
Navier - Stokes equation.
Finally , in Chapter 4 we will prove the existence of weak solutions in three
dimensions (Hopf theorem) , with the Aubin -Lions lemma and we shall
prove the strong energy inequality for the Leray -Hopf weak solutions.
Main subject category:
Science
Keywords:
The Navier- Stokes Equation , Fluid Dynamics
