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 evolution dam problem for nonlinear Darcy's law and Dirichlet boundary conditions.
The evolution Darcy-Boussinesq system (a weak maximum principle and the uniqueness)
The Exact Analytical Solution for the Gas Lubricated Bearing in the Slip and Continuum Flow Regime
The existence and uniqueness of solutions of equations for ideal compressible polytropic fluids.
The existence of an exponential attractor in magneto-micropolar fluid flow via the ℓ-trajectories method
We consider the magneto-micropolar fluid flow in a bounded domain Ω ⊂ ℝ². The flow is modelled by a system of PDEs, a generalisation of the two-dimensional Navier-Stokes equations. Using the Galerkin method we prove the existence and uniqueness of weak solutions and then using the ℓ-trajectories method we prove the existence of the exponential attractor in the dynamical system associated with the model.
The existence of global solutions to the elliptic-hyperbolic Davey-Stewartson system with small initial data
The far-field modelling of transonic compressible flows
We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...
The finite element method with nodes moving along the characteristics for convection-diffusion equations.
The finite volume method for an elliptic-parabolic equation.
The flow of a non-Newtonian fluid induced due to the oscillations of a porous plate.
The Fluid Flow Through Porous Media. Regularity of the Free Surface.
The fluid profile during spin-coating over a small sinusoidal topography.
The four positive vortices problem : regions of chaotic behavior and the non-integrability
The Gauss center research in multiscale scientific computation.
The generalized finite volume SUSHI scheme for the discretization of the peaceman model
We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later,...
The global existence of weak solutions of the mollified system of equations of motion of viscous compressible fluid
The grazing collisions asymptotics of the non cut-off Kac equation
The Helmholtz decomposition in arbitrary unbounded domains - a theory beyond