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SUMMARY:Flora Philipp
DTSTART:20251126T080000Z
DTEND:20251126T090000Z
DTSTAMP:20260422T122511Z
UID:MathMAC/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathMAC/45/"
 >Global Existence of Weak Solutions to Chemotaxis Navier-Stokes-Korteweg s
 ystems</a>\nby Flora Philipp as part of Modelling of materials - theory\, 
 model reduction and efficient numerical methods (UNCE MathMAC)\n\n\nAbstra
 ct\nA Chemotaxis compressible Navier–Stokes model was introduced to desc
 ribe vascular network formation. Global existence for this system was rece
 ntly shown for adiabatic exponent $\\gamma>8/5$ by Huo and\nJ\\“ungel. W
 e regularize the equations by adding a Korteweg term and prove global exis
 tence for the regularized system\, allowing for smaller adiabatic exponent
 s ($\\gamma>1$). Our analysis is based on the use of a free energy as well
  as the BD-entropy\, and exploits additional regularity properties derived
  via the systematic integration-by-parts technique introduced by J\\“ung
 el and Matthes. In the course of this\, we can also establish existence re
 sults for a broader class of Navier–Stokes–Korteweg systems\, which un
 til now have only been investigated in two special cases: the Quantum-Navi
 er–Stokes equation\nand the thin film equation.\n
LOCATION:https://researchseminars.org/talk/MathMAC/45/
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