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SUMMARY:Jinkai Li (华南师范大学)
DTSTART:20201228T074500Z
DTEND:20201228T083000Z
DTSTAMP:20260423T005800Z
UID:iccm2020/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/iccm2020/60/
 ">Well-posedness of entropy-bounded solutions of the compressible Navier-S
 tokes equations with vacuum</a>\nby Jinkai Li (华南师范大学) as part
  of ICCM 2020\n\n\nAbstract\nThe entropy is one of the fundamental physica
 l states of a fluid. For the ideal gases\, the entropy can be expressed as
  some linear combination of the logarithms of the density and temperature 
 in the non-vacuum region\, and\, in the viscous case\, the equation that i
 t satisfies is highly singular in the region close to the vacuum. Due to t
 he singularity of the logarithmic function at zero\, which may lead to the
  singularity of the entropy\, and the singularity of the entropy equation 
 near the vacuum region\, in spite of its importance in the gas dynamics\, 
 the mathematical analyses on the behavior of the entropy near the vacuum r
 egion\, were rarely carried out\; in particular\, in the presence of vacuu
 m\, it was unknown if the entropy remains its boundedness. We will show in
  this talk that the ideal gases retain their uniform boundedness of the en
 tropy\, locally or globally in time\, if the vacuum occurs at the far fiel
 d only and the density decays slowly enough at the far field. Precisely\, 
 we consider the Cauchy problem to the full compressible Navier-Stokes equa
 tions\, with or without heat conductivity\, and establish the local and gl
 obal existence and uniqueness of entropy-bounded solutions in the presence
  of vacuum at the far field only. These are joint works with Prof. Zhou
 ping Xin.\n
LOCATION:https://researchseminars.org/talk/iccm2020/60/
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