Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension
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2010
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1268414323 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-osu12684143232021-08-03T05:58:47Z Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension Ye, Ji Mathematics <p>My current research concernsglobal existence for arbitrary nonzero surface tension ofbubbles in a Hele-Shaw cell.</p><p>Without imposed pressure gradient or side walls, the circular bubble is shown to beasymptotically stable to all sufficiently smooth initial perturbation.</p><p>For the bubbles translating in the presence of a pressure, when the cell width to bubble size is sufficiently large,we show that a unique steady translating near-circular bubble symmetricabout the channel centerline exists, where the bubble translation speed inthe laboratory frame is foundas part of the solution.We proveglobal existence for symmetric sufficiently smooth initial conditionsclose to this shape and show that the steady translatingbubble solution is an attractor within this class of disturbances.In the absence of side walls, we prove stability of the steadytranslating circular bubble without restrictionon symmetry of initial conditions.These results hold for anynonzero surface tension despite the fact that a local planar approximationnear the front of the bubble would suggestSaffman-Taylor instability. An important element of the proof wasthe introduction of a weighted Sobolev norm thataccounts for stabilization due to advection of disturbancesfrom the front to the back of the bubble.</p><p>We exploit a boundary integral approachthat is particularly suitable for analysis of nonzero viscosity ratiobetween fluid inside and outside the bubble.</p> 2010-08-24 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1268414323 http://rave.ohiolink.edu/etdc/view?acc_num=osu1268414323 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
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NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics Ye, Ji Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension |
| author |
Ye, Ji |
| author_facet |
Ye, Ji |
| author_sort |
Ye, Ji |
| title |
Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension |
| title_short |
Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension |
| title_full |
Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension |
| title_fullStr |
Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension |
| title_full_unstemmed |
Global existence for bubbles in a Hele-Shaw cell with arbitrary nonzero surface tension |
| title_sort |
global existence for bubbles in a hele-shaw cell with arbitrary nonzero surface tension |
| publisher |
The Ohio State University / OhioLINK |
| publishDate |
2010 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1268414323 |
| work_keys_str_mv |
AT yeji globalexistenceforbubblesinaheleshawcellwitharbitrarynonzerosurfacetension |
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1719428843131895808 |