The objective of this work is to investigate the time discretization of two dimensional Navier-Stokes system with the slip boundary conditions. First, the existence of weak solutions for a fixed time step 4t > 0 is presented and then the limit passage as 4t → 0 is carried out. The proof is based on a new technique established for the steady Navier-Stokes equations by Mucha P. B. and Pokorný M. ...

We derive estimates on the upper bounds of the asymptotic degrees of freedom for strong solutions of the two-dimensional Navier–Stokes equations with no-slip and nonhomogeneous boundary conditions. The analysis is also extended to an abstract equation modelling some other equations in fluid mechanics. Similar results are obtained. AMS classification scheme numbers: 35Q30, 37L30, 76D05

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained.

We consider a family of solutions to the evolutionary Navier-Stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries. We give a complete description of the asymptotic limit by means of Γ−convergence arguments, and identify a general class of boundary conditions.

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. We derive the relative entropy inequality in the spirit of [7] for the system on moving domain and use it to prove the weak-strong uniqueness property.

We have experimentally observed the forms of splash caused by spheres diving into water, where the spheres are made of hydro-gel or acrylic resin[1]. The experimental results have shown that the splash by the hydro-gel sphere has formed the crown-type one, whereas the acrylic sphere formed the column-type one despite the same experimental condition. This means that the surface condition of wall...

In immiscible two-phase flows, the contact line denotes the intersection of the fluid– fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The rec...

Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Na...

Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is computed by MD simulations. We describe laminar flow away from a curved boundar...