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Grantor: Czech Science Foundation

**Objectives**:

Equations of compressible viscous fluids are important models in many applications. We will study the corresponding systems of partial differential equations from several points of view: existence theory and qualitative properties of solutions for different choices of boundary conditions (including open system), different types of domains (in particular varying in time), different types of solutions (weak, strong, dissipative) and different simplified models (in

particular, compressible primitive equations) as well as from the point of view of numerical mathematics (construction of benchmarks, numerical analysis of some methods, comparision of different numerical methods). The proposal of the project is based on a close collaboration of specialists from different mathematical disciplines.

Main investigator:

IM team members:

Bodnár Tomáš Caggio Matteo Kalousek Martin Kračmar Stanislav Kreml Ondřej |
Mácha Václav Neustupa Jiří Oschmann Florian Radoševič Ana Vacek Karel |

Participating institutions:

Institute of Mathematics, Czech Academy of Sciences(**Coordinator**)

Faculty of Mathematics and Physics, Charles University, Prague