Recent Developments of Mathematical Fluid Mechanics

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:
1) 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.

The book addresses recent developments of the mathematical research on the Navier-Stokes and Euler equations

as well as on related problems. In particular, there are covered:

1) existence, uniqueness, and the regularity of weak solutions;

2) stability of the motion in rest and the asymptotic behavior of solutions;

3) singularity and blow-up of weak and strong solutions;

5) motions of rotating fluids, or of fluids surrounding a rotating body;

6) free boundary problems;

7) maximal regularity theory and other abstract results for mathematical fluid mechanics.

For this quarter century, these topics have been playing a central role in both pure and applied mathematics

and having a great influence to the developm

There are 24 articles in this book in which the nonlinear PDE arising in the fluid mechanics are

mainly discussed.

The authors consist of speakers and participants of the

"International Conference on the Mathematical Fluid Dynamics"

on the occasion of Professor Yoshihiro Shibatas 60th birthday held

on March 5--9 in 2013 at old capital city Nara, Japan.