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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:The Muskat problem on the half-plane models motion of an interface between 
 two fluids of distinct densities in a porous medium that sits atop an imper
 meable layer, such as oil and water in an aquifer above bedrock.  We show t
 hat unlike on the whole plane, finite time singularities do arise in the st
 able regime (lighter fluid above the heavier one) in this setting, includin
 g from arbitrarily small smooth initial data.  We achieve this by developin
 g a local well-posedness theory for this model as well as obtaining maximum
  principles for the height, slope, and potential energy of the fluid interf
 ace.  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 impermeable layer, and includes considerably mo
 re general fluid interface geometries than even previous whole plane result
 s.\n
X-ALT-DESC;FMTTYPE=text/html:<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:20260921T193754
DTSTART;TZID=America/New_York:20240926T150000
DTEND;TZID=America/New_York:20240926T160000
SEQUENCE:0
TRANSP:OPAQUE
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