Recent Developments of Mathematical Fluid Mechanics

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Herbert Amann, Yoshikazu Giga, Hideo Kozono, Hisashi Okamoto, Masao Yamazaki
Birkhäuser, Mar 17, 2016 - Mathematics - 482 pages

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.

 

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Contents

The Work of Yoshihiro Shibata
1
Existence of Weak Solutions for a Diffuse Interface Model of PowerLaw Type TwoPhase Flows
13
Stationary Solutions for a NavierStokesCahnHilliard System with Singular Free Energies
24
Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems
43
A Generalization of Some Regularity Criteria to the NavierStokes Equations Involving One Velocity Component
78
The GradientSymmetric Case
99
Thermodynamically Consistent Modeling for DissolutionGrowth of Bubbles in an Incompressible Solvent
110
On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary
135
On the Conjecture That μm
257
Bounded Analyticity of the Stokes Semigroup on Spaces of Bounded Functions
274
On the Weak Solution of the FluidStructure Interaction Problem for ShearDependent Fluids
291
Stability of Time Periodic Solutions for the Rotating NavierStokes Equations
320
Weighted LpLq Estimates of Stokes Semigroup in HalfSpace and Its Application to the NavierStokes Equations
337
On Vorticity Formulation for Viscous Incompressible Flows in R3+
350
A Weak Solution to the NavierStokes System with Naviers Boundary Condition in a TimeVarying Domain
375
Effects of FluidBoundary Interaction on the Stability of Boundary Layers in Plasma Physics
401

Inhomogeneous Boundary Value Problems in Spaces of Higher Regularity
157
BlowUp Criterion for 3D NavierStokes Equations and LandauLifshitz System in a Bounded Domain
175
Local Regularity Results for the Instationary NavierStokes Equations Based on Besov Space Type Criteria
183
On Global WellIllPosedness of the EulerPoisson System
215
On the Motion of a LiquidFilled Rigid Body Subject to a TimePeriodic Torque
232
On Incompressible TwoPhase Flows with Phase Transitions and Variable Surface Tension
411
On the NashMoser Iteration Technique
443
Rate of Convergence to the Stationary Solution of the NavierStokes Exterior Problem
459
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