The 3D Happel model for complete isotropic Stokes flow.
The 3D navier-stokes equations seen as a perturbation of the 2D navier-stokes equations
The Asymptotics of the Heat Equation for a Boundary Value Problem.
The basic boundary value problems of static elasticity theory and their Cosserat spectrum.
The Blasius function in the complex plane.
The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure
We assume that is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of .
The Cauchy problem and decay rates for strong solutions of a Boussinesq system.
The Cauchy problem for the homogeneous time-dependent Oseen system in : spatial decay of the velocity
We consider the homogeneous time-dependent Oseen system in the whole space . The initial data is assumed to behave as , and its gradient as , when tends to infinity, where is a fixed positive number. Then we show that the velocity decays according to the equation , and its spatial gradient decreases with the rate , for tending to infinity, uniformly with respect to the time variable . Since these decay rates are optimal even in the stationary case, they should also be the best possible...
The Cauchy problem for viscous shallow water equations.
In this paper we study the Cauchy problem for viscous shallow water equations. We work in the Sobolev spaces of index s > 2 to obtain local solutions for any initial data, and global solutions for small initial data.
The Cauchy-Poisson waves in an inviscid rotating stratified liquid.
The conditioning of the stiffness matrix for certain elements approximating the incompressibility condition in fluid dynamics.
The Convergence of two Numerical Schemes for the Navier-Stokes Equations.
The Effect of Crystal-Melt Surface Energy on the Stability of Ultra-Thin Melt Films
The stability and evolution of very thin, single component, metallic-melt films is studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the film. Linear analysis reveals that there is a maximum applied far-field temperature in the gas, beyond which there is no film instability. Instabilities...
The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics
The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.
The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop.
The equations of viscous incompressible nonhomogeneous fluids in noncylindrical domains: on the existence and regularity
We prove the existence of a weak solution and of a strong solution (locally in time) of the equations which govern the motion of viscous incompressible non-homogeneous fluids. Then we discuss the decay problem.
The equilibrium configuration of liquid drops.
The Eulerian limit and the slip boundary conditions-admissible irregularity of the boundary
We investigate the inviscid limit for the stationary Navier-Stokes equations in a two dimensional bounded domain with slip boundary conditions admitting nontrivial inflow across the boundary. We analyze admissible regularity of the boundary necessary to obtain convergence to a solution of the Euler system. The main result says that the boundary of the domain must be at least C²-piecewise smooth with possible interior angles between regular components less than π.
The Exact Analytical Solution for the Gas Lubricated Bearing in the Slip and Continuum Flow Regime
The fluid profile during spin-coating over a small sinusoidal topography.