Recent Developments of Mathematical Fluid Mechanics

✍ Scribed by Herbert Amann, Yoshikazu Giga, Hideo Kozono, Hisashi Okamoto, Masao Yamazaki (eds.)

• Publisher: Birkhäuser Basel
• Year: 2016
• Tongue: English
• Leaves: 478
• Series: Advances in Mathematical Fluid Mechanics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-ix
The Work of Yoshihiro Shibata....Pages 1-12
Existence of Weak Solutions for a Diffuse Interface Model of Power-Law Type Two-Phase Flows....Pages 13-23
Stationary Solutions for a Navier-Stokes/Cahn-Hilliard System with Singular Free Energies....Pages 25-41
Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems....Pages 43-77
A Generalization of Some Regularity Criteria to the Navier–Stokes Equations Involving One Velocity Component....Pages 79-97
On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case....Pages 99-109
Thermodynamically Consistent Modeling for Dissolution/Growth of Bubbles in an Incompressible Solvent....Pages 111-134
On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary....Pages 135-156
Inhomogeneous Boundary Value Problems in Spaces of Higher Regularity....Pages 157-173
Blow-Up Criterion for 3D Navier-Stokes Equations and Landau-Lifshitz System in a Bounded Domain....Pages 175-182
Local Regularity Results for the Instationary Navier-Stokes Equations Based on Besov Space Type Criteria....Pages 183-214
On Global Well/Ill-Posedness of the Euler-Poisson System....Pages 215-231
On the Motion of a Liquid-Filled Rigid Body Subject to a Time-Periodic Torque....Pages 233-255
Bounded Analyticity of the Stokes Semigroup on Spaces of Bounded Functions....Pages 257-273
On the Weak Solution of the Fluid-Structure Interaction Problem for Shear-Dependent Fluids....Pages 275-289
Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations....Pages 291-319
A Weak Solution to the Navier–Stokes System with Navier’s Boundary Condition in a Time-Varying Domain....Pages 321-335
Effects of Fluid-Boundary Interaction on the Stability of Boundary Layers in Plasma Physics....Pages 337-349
On Incompressible Two-Phase Flows with Phase Transitions and Variable Surface Tension....Pages 351-374
On the Nash-Moser Iteration Technique....Pages 375-400
Rate of Convergence to the Stationary Solution of the Navier-Stokes Exterior Problem....Pages 401-410
....Pages 411-442

✦ Subjects

Partial Differential Equations