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SUMMARY:Sourav Mitra (Institute of Mathematics\, Czech Academy of Sciences
 )
DTSTART:20221212T144000Z
DTEND:20221212T161000Z
DTSTAMP:20260405T174548Z
UID:NSCM/95
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NSCM/95/">Ex
 istence of a weak solution for a compressible multicomponent fluid-structu
 re interaction problem</a>\nby Sourav Mitra (Institute of Mathematics\, Cz
 ech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics\
 n\nLecture held in Room K3\,  Faculty of Mathematics and Physics\, Charles
  University\, Sokolovská 83  Prague 8..\n\nAbstract\nI will speak about o
 ur recent work on the analysis of a system of PDEs governing the interacti
 on between two compressible mutually noninteracting fluids and a shell of 
 Koiter type encompassing a time-dependent 3D domain filled by the fluids. 
 The dynamics of the fluids is modeled by compressible\nNavier-Stokes equat
 ions with a physically realistic pressure depending on the densities of bo
 th fluids. The shell constitutes the boundary of the fluid domain\, and it
  possesses a non-linear\, non-convex Koiter energy (of a quite general for
 m). We are interested in the existence of a weak solution to the system\nu
 ntil the time-dependent boundary approaches a self-intersection. We first 
 prove a global existence result (until a degeneracy occurs) when the adiab
 atic exponents solve max{γ\, β} > 2 and min{γ\, β} > 0\, and further\,
  the densities are comparable. Next\, with a slightly extra regularity ass
 umption on the\ninitial structural displacement\, we extend our global exi
 stence result to the case max{γ\, β} ≥ 2 and min{γ\, β} > 0.\nIn the
  first part of the talk\, I will try to introduce the classical theory on 
 the existence of weak solutions for compressible mono-fluid models. Next\,
  I will talk about our work on the multi-component FSI problem. This is jo
 int work with M. Kalousek and Š. Nečasová.\n
LOCATION:https://researchseminars.org/talk/NSCM/95/
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