The aim of this proceeding is addressed to present recent developments
of the mathematical research on the Navier-Stokes equations, the Euler
equations and other related equations. In particular, we are interested
in such problems as:
- existence, uniqueness and regularity of weak solutions2) stability
and its asymptotic behavior of the rest motion and the steady state3)
singularity and blow-up of weak and strong solutions4) vorticity and
energy conservation5) fluid motions around the rotating axis or outside
of the rotating body6) free boundary problems7) maximal regularity
theorem and other abstract theorems for mathematical fluid mechanics.