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Grantor: Ministry of Education, Youth and Sports - MMT

The goal of the project is studying qualitative properties of a particular class of the so-called energetically weak solutions to complex system of the Navier-Stokes-Fourier type as well as Coupling of these systems with the phase transition equations of the Cahn-Hilliard or Allen-Cahn type. We plan to investigate these problems also in unbounded physical domains in appropriate classes of uniformly bounded functions.

The main goal is obtaining new results in the following directions:

• applications of the relative entropy methods and the consequences concerning stability of the so-called dissipative solutions

• singular limits, in particular the sharp interface limits with rigorous mathematical justification

• long-time dynamics, with a particular emphasis on the existence of bounded absorbing sets, asymptotic compactness of greajectories and the relevant questions concerning the attractors and their structure and complexity

Main investigator:

IM team members:

Michálek Martin |

Participating institutions:

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

Faculty of Mathematics and Physics, Charles University