Navier-Stokes equations: weak solution, its uniqueness and regularity

Abstract

This paper is a brief intorduction to the study of properties of weak solutions to the evolutionary incompressible Navier-Stokes equations. First, several types of solutions are introduced as well as relations between them.

Then the paper deals with weak solution, its existence, uniqueness and regularity in different situations as well as with the conditional regularity (regularity criteria).

Keywords

• incompressible Navier-Stokes equations
• weak solution
• uniqueness
• regularity of solutions
• regularity criteria