Recent Developments of Mathematical Fluid Mechanics [Hardcover]

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 Work of Yoshihiro Shibata, Herbert Amann, Yoshikazu Giga, Hisashi Okamoto, Hideo Kozono and Masao Yamazaki.- Existence of weak solutions for a diffuse interface model of power-law type two-phase flows, Helmut Abels, Lars Diening and Yutaka Terasawa.- Stationary Solutions for a Navier-Stokes/Cahn- Hilliard System with Singular Free Energies, Helmut Abels and Josef Weber.- Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems, Herbert Amann.- A generalization of some regularity criteria to the NavierStokes equations involving one velocity component, Simon Axmann and Milan Pokorny.- On the singular p-Laplacian system under Navier slip type boundary conditions, The gradient-symmetric case,
H. Beir?o da Veiga.- Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent, Dieter Bothe and Kohei Soga.- On unsteady internal flows of Bingham fluids subject to threshold slip on the impermeable boundary, Miroslav Bul?1ek and Josef M?lek.- Inhomogeneous boundary value problems in spaces of higher regularity,Robert Denk and Tim Seger.- Blow-up criterion for 3D Navier-Stokes equations and Landau-Lifshitz System in a bounded domain, Jishan Fan and Tohru Ozawa.- Local Regularity Results for the Inl£P