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UID:6f8ed1ad6cb9ba2d1841c7a5e048fa40
CATEGORIES:Joint Princeton-Rutgers Seminar on Analysis of Fluids
CREATED:20240831T161027
SUMMARY:Andrej Zlatos: Stable regime singularity for the Muskat problem
LOCATION:Fine Hall 314\, Princeton University
DESCRIPTION:<p style="font-size: 16px; font-weight: 400; letter-spacing: normal; text-a
 lign: start; text-indent: 0px; text-transform: none; white-space: normal; w
 ord-spacing: 0px; text-decoration: none; margin: 0px 0px 12px; color: #3333
 33; font-family: franklin_gothic, sans-serif; orphans: 2; widows: 2; backgr
 ound-color: #ffffff;">The Muskat problem on the half-plane models motion of
  an interface between two fluids of distinct densities in a porous medium t
 hat sits atop an impermeable layer, such as oil and water in an aquifer abo
 ve bedrock. &nbsp;We show that unlike on the whole plane, finite time singu
 larities do arise in the stable regime (lighter fluid above the heavier one
 ) in this setting, including from arbitrarily small smooth initial data. &n
 bsp;We achieve this by developing a local well-posedness theory for this mo
 del as well as obtaining maximum principles for the height, slope, and pote
 ntial energy of the fluid interface. &nbsp;The former allows the interface 
 to touch the bottom, which applies to the important scenario of the heavier
  fluid invading a region occupied by the lighter fluid along the impermeabl
 e layer, and includes considerably more general fluid interface geometries 
 than even previous whole plane results.</p>
CONTACT:University of California San Diego
DTSTAMP:20260921T211132
DTSTART;TZID=America/New_York:20240926T150000
DTEND;TZID=America/New_York:20240926T160000
SEQUENCE:0
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