The $n$-Dimensional Incompressible Navier-Stokes Equations: A Survey of Recent Advances

Source abstract

Consider the Cauchy problem for the $n$-dimensional incompressible Navier-Stokes equations. There have been very interesting advances on the mathematical influences of physical mechanisms on the global smooth solutions (if the dimension $n=2$) and the global weak solutions (if the dimension $n\geq 3$) of the Navier-Stokes equations. This paper is a simple survey of recent advances on the properties of the solutions.