Navier—Stokes Equations and Related Nonlinear Problems

Front Matter....Pages i-ix
Front Matter....Pages 1-1
On the Stability of a Flow Between Two Vertical Planes Caused by Homogeneous Heat Source and Pressure Gradient....Pages 3-9
Stability of Solutions of Parabolic Equations by a Combination of the Semigroup Theory and the Energy Method....Pages 11-22
Steady Flow of a Viscous Incompressible Fluid in an Unbounded “Funnel-Shaped” Domain....Pages 23-31
Weighted L q -Theory and Pointwise Estimates for Steady Stokes and Navier-Stokes Equations in Domains with Exit to Infinity....Pages 33-51
Generalized Solutions for the Stokes Equation in Exterior Domains....Pages 53-62
On the Existence of Periodic Weak Solutions on the Navier-Stokes Equations in Exterior Regions with Periodically Moving Boundaries....Pages 63-73
(2 + k )-Solutions in L q to the Dirichlet and Neumann Problem for Δ and for Stokes’ System in Exterior Domains....Pages 75-104
The Weak Neumann Problem and the Helmholtz Decomposition of Two-Dimensional Vector Fields in Weighted L ϒ -Spaces....Pages 105-116
Boundary Integral Equations for the Stokes Problem in Exterior Domains of ℝ n ....Pages 117-127
Front Matter....Pages 129-129
Regular Solutions to the Steady Navier-Stokes Equations....Pages 131-139
A Note on Derivative Estimates for a Hopf Solution to the Navier-Stokes System in a Three-Dimensional Cube....Pages 141-146
Classical Solution to the Navier-Stokes System....Pages 147-152
Front Matter....Pages 153-153
The Maximum Principle for the Equation of Continuity of Compressible Media....Pages 155-163
Uniqueness of Weak Solutions of Unsteady Motions of Viscous Compressible Fluids (II)....Pages 165-170
On the Existence of Steady Motions of a Viscous Isothermal Fluid in a Pipe....Pages 171-188
Front Matter....Pages 189-189
Classical Solvability of the Problem Describing the Evolution of a Drop in a Liquid Medium....Pages 191-199
Analysis of a Nonisothermal Viscous Flow Problem with Free Boundaries and a Dynamic Contact Line....Pages 201-210
On the Free Boundary Problem for the Navier-Stokes Equations Governing the Motion of a Viscous Incompressible Fluid in a Slowly Rotating Container....Pages 211-227
Front Matter....Pages 229-229
Heat-Conducting Incompressible Viscous Fluids....Pages 231-243
On a Class of Abstract Evolution Equations Related to the Motion of Complexity 2 Fluids....Pages 245-258
Front Matter....Pages 229-229
Asymptotic in Time Decay of Solutions to the Equations of a Second-Grade Fluid Filling the Whole Space....Pages 259-271
On Boundary Conditions for Fluids of the Differential Type....Pages 273-278
Thermoconvection with Dissipation of Quasi-Newtonian Fluids in Tubes....Pages 279-288
Front Matter....Pages 289-289
Remarks on the Flow of Holes and Electrons in Crystalline Semiconductors....Pages 291-306
Bifurcation of Solutions to Reaction-Diffusion Systems with Unilateral Conditions....Pages 307-322
Stability Theory for Flows Governed by Implicit Evolution Equations....Pages 323-332
Front Matter....Pages 333-333
A Vorticity Creation Algorithm for the Navier-Stokes Equations in Arbitrary Domain....Pages 335-349
Negative Isotropic Eddy Viscosity: A Common Phenomenon in two Dimensions....Pages 351-355
A Particle in Cell Method for the Isentropic Gas Dynamic System....Pages 357-365
Domain Decomposition Methods for Fluid Dynamics....Pages 367-376
A Regularizing Property of Rothe’s Method to the Navier-Stokes Equations....Pages 377-391
Simulation of Multiple Free Surface Transient Newtonian and Non-Newtonian Flows....Pages 393-402
Back Matter....Pages 403-406