Nečas Center for Mathematical Modeling Boundary Trace Inequalities and Rearrangements

Nečas Center for Mathematical Modeling Asymptotic properties of solutions to the equations of incompressible fluid mechanics

Well-accepted hypothesis in the fluid dynamics is that if the boundary of the physical domain is impermeable then the viscous fluid adheres completely to it. Many authors recently proposed mathematical justifications for this hypothesis using the so-called rugous boundary. In this Paper we want to discuss optimality of results obtained in Bucur et al. [3], Bucur and Feireisl [4] or Dı́az et al. ...

Nečas Center for Mathematical Modeling Optimal L∞(L2)-error estimates for the DG method applied to nonlinear convection–diffusion problems with nonlinear diffusion

Nečas Center for Mathematical Modeling On Pressure Boundary Conditions for Steady Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities

We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the surface force at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and the uniqueness of w...

Nečas Center for Mathematical Modeling Low Mach number limit for the Navier-Stokes system on unbounded domains under strong stratification

Nečas Center for Mathematical Modeling Anisotropic Diffusion in Mathematical Visualization

We propose a method of vector field visualization based on noisy texture smearing. The smearing process is carried out by solving a problem for the Allen-Cahn diffusion PDE with advection. We introduce a parallel algorithm for the numerical solution of the given problem and we present several results of the efficiency benchmark. Finally, an extension to diffusion tensor field visualization is c...