Šárka Nečasová

Grants
- Flow of fluids in domains with variable geometry (P201/11/1304)
  from 01/01/2011 to 31/12/2013 main investigator
- The goal of the project is to get new relevant results concerning flow in domains with varying geometry. From the viewpoint of theoretical analysis, we will deal with flow of fluids (incompressible and compressible) around a rotating body (existence of weak or very weak solutions, asymptotic behaviour solutions, artificial boundary conditions) in case that the axis of rotation of the body and the velocity at infinity are parallel or not parallel. We will also investigate the related hydrodynamical potential theory. Moreover, we will investigate the case of motion of rigid bodies in viscous fluid (mostrly non-Newtonian incompressible and Newtonian compressible), in several cases we include the changes of temperature. Part of the problems mentioned above will be solved numerically. Finally, we perform the numerical simulation of flow of fluids in domains with complicated geometry corresponding to the flow of blood in healthy veins as well as in cases of cardiovascular diseases.
- The motion of rigid bodies in liquid: mathematical analysis, numerical simulation and related problems (IAA100190804)
  from 01/01/2008 to 31/12/2010 main investigator
- In the framework of the project we will study the steady flow around bodies. We will consider the case when the direction of the angular velocity and of the velocity at infinity are or are not parallel. We will extend the results from the previous project, where the angular and tranlation velocities were parallel. We will study the linear cases and Navier-Stokes equations. We will investigate the existence of solution, asymptotic behaviour, resolvent and spectrum problem. Further, we will study the motion of several bodies in the fluid. We will consider the influence of boundary conditions and possibility of collisions. In this part we will study the existence of weak solution for steady and non-steady cases. We will investigate fluid flows described by Navier-Stokes equations as well as by non-Newtonian models. We will investigate the modeling of blood flow and related cardiovascular cases. Next to it the numerical simulation of severeal models will be performed.
- Qualitative analysis and numerical solution of flow problems (201/08/0012)
  from 01/01/2008 to 31/12/2012 investigator
- Mathematical modelling of fluid flows in different regimes.
- Nečas Center for Mathematical Modeling - part IM (LC06052)
  from 01/01/2006 to 31/12/2011 investigator
- The general goal of the Nečas Center for Mathematical Modeling is to establish a significant scientific team in the field of mathematical properties of models in continuum mechanics and thermodynamics, developed by an intensive collaboration of five important research teams at three Prague affiliations and their goal-directed collaboration with top experts from abroad. The research projects of the center include: 1) Nonlinear theoretical, numerical and computer analysis of problems of continuum physics. 2) Heat-conductive and deforming processes in compressible fluids, incompressible substances of fluid type, and in linearly elastic matters. 3) Interaction of the substances. 4) Biochemical procedures in substances. 5) Passages between models, dimensional analysis.
- Mathematical modelling of motion of bodies in Newtonian and non-Newtonian fluids and related mathematical problems (IAA100190505)
  from 01/01/2005 to 01/12/2007 main investigator
- Investigation of properties of models describing motion of rigid bodies in viscous fluid. Existence of weak and strong solutions, asymptotic behaviour, attainability, numerical analysis and solution of selected models.