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SUMMARY:Bogdan-Vasile Matioc (University of Regensburg)
DTSTART:20200709T140000Z
DTEND:20200709T145000Z
DTSTAMP:20260423T035611Z
UID:IMS/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/38/">The
  Muskat problem in subcritical Lp-Sobolev spaces</a>\nby Bogdan-Vasile Mat
 ioc (University of Regensburg) as part of PDE seminar via Zoom\n\n\nAbstra
 ct\nThe Muskat problem is a classical mathematical model which describes t
 he motion of two immiscible and incompressible Newtonian fluids in an homo
 geneous porous medium. The mathematical model posed in the entire plane ca
 n be formulated as an evolution equation for the function that parametrize
 s the free boundary between the fluids. When neglecting surface tension ef
 fects\, the evolution equation is fully nonlinear and nonlocal and it invo
 lves singular integral operators defined by kernels that depend nonlinearl
 y on the unknown. We prove that the evolution problem is of parabolic type
  in the regime where the Rayleigh-Taylor condition is satisfied. Based upo
 n this feature we establish the well posedness of the Muskat problem in al
 l subcritical Lp-Sobolev spaces together with a parabolic smoothing proper
 ty. This is a joint work with Helmut Abels.\n
LOCATION:https://researchseminars.org/talk/IMS/38/
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