WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS

(整期优先)网络出版时间:2014-01-11
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Themainpurposeofthispaperistwo-fold:(i)togeneralizeanexistenceresultforacompressiblegas-liquidmodelwithafrictiontermrecentlypublishedbyFriisandEvje[SIAMJ.Appl.Math.,71(2011),pp.2014–2047];(ii)toderiveauniquenessresultforthesamemodel.Amainingredientintheexistencepartistheobservationthatwecanconsiderweakerassumptionsontheinitialliquidandgasmass,andstillobtainanexistenceresult.Comparedtotheabovementionedwork,werelyonamorerefinedapplicationoftheestimatesprovidedbythebasicenergyestimate.Concerningtheuniquenessresult,weborrowideasfromFangandZhang[NonlinearAnal.TMA,58(2004),pp.719–731]andderiveastabilityresultunderappropriateconstraintsonparametersthatdeterminerateofdecaytowardzeroattheboundaryforgasandliquidmasses,andgrowthrateofmassesassociatedwiththefrictiontermandviscouscoefficient.