Recent Developments of Mathematical Fluid Mechanics

Abstract

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 Navier-Stokes 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. Beirao 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 Bulicek and Josef Malek.- 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 Instationary Navier-Stokes Equations Based on Besov Space Type Criteria, Reinhard Farwig.- On global well/ill-posedness of the Euler-Poisson system, Eduard Feireisl.- On the Motion of a Liquid- Filled Rigid Body Subject to a Time-Periodic Torque, Giovanni P. Galdi, Giusy Mazzone and Mahdi Mohebbi.- Seeking a proof of Xie's inequality: on the conjecture that m ! 1, John G. Heywood.- Bounded Analyticity of the Stokes Semigroup on Spaces of Bounded Functions, Matthias Hieber and Paolo Maremonti.- On the weak solution of the fluid-structure interaction problem for sheardependent fluids, Anna Hundertmark, Maria Lukacova-Medvid'ova and Sarka Necasova.- Stability of time periodic solutions for the rotating Navier-Stokes equations, Tsukasa Iwabuchi, Alex Mahalov and Ryo Takada.- Weighted Lp - Lq estimates of Stokes semigroup in half-space and its application to the Navier-Stokes equations,Takayuki Kobayashi and Takayuki Kubo.- On vorticity formulation for viscous incompressible flows in R3+, Humiya Kosaka and Yasunori Maekawa.- A Weak Solution to the Navier-Stokes System with Navier's Boundary Condition in a Time-Varying Domain, Jiri Neustupa and Patrick Penel.- Effects of fluid-boundary interaction on the stability of boundary layers in plasma physics, Masashi Ohnawa.- On Incompressible Two-Phase Flows with Phase Transitions and Variable Surface Tension, Masao Yamazaki.