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Grantor: Ministry of Education, Youth and Sports - MMT

**Objectives:**

**G1.** *Global existence of weak solution of full system in time-dependent domain*.

**Goals:** Our goals is the study of the global existence of a weak solution in the case of a bounded or an exterior domains for the Navier or Dirichlet type of boundary conditions. We will use the method introduced in *E. Feireisl: Dynamics of viscous compressible fluids, 2004* for fixed domain and we will also apply the penalization method.

**G2:** *Relative entropy inequality.*

**Goals:** We will focus on the derivation of the relative entropy inequality in the case of time-dependent domain. We will use the results from fixed domain introduced in *E. Feireisl and A. Novotný: Weak-strong uniqueness for the full Navier-Stokes-Fourier system, 2012*.

**G3.** *Singular limits*.

**Goals** We shall study the singular limits in the regime of low Mach number. From this follows that the limit system (target system) is the system of incompressible flow in the time-dependent domain. We will use the results from *E. Feireisl, O. Kreml, Š. Nečasová, J. Neustupa, J. Stebel: Incompressible limits of fluids excited by moving boundaries, 2014*, where barotropic case was studied, and also the results for fixed domains.

**G4:** *Weak solution of viscous flow around rotating rigid **body and his asymptotic behavior.*

**Goals:** We will focus on the problem of existence of weak solution in weighted Lorentz spaces to get the asymptotic behavior of flow around a body. Because of the lack of the regularity in L^{p} spaces it is necessary to go into more complicated structure of Lorentz spaces, where the integrability of convective term is satisfied. Moreover, we would like to study the relative entropy inequality in the case of compressible flow around rotating body.

Main investigator:

IM team members:

Kreml Ondřej |
Mácha Václav |

Participating institutions:

Institute of Mathematics, Czech Academy of Sciences

Institute of Mathematics, Polish Academy of Sciences