應用中的偏微分方程線上研討咨詢會

應用中的偏微分方程線上研討咨詢會會議日程復旦大學數(shù)學科學學院、復旦大學應用數(shù)學中心、上海市現(xiàn)代應用數(shù)學重點實驗室11月29日（周三）騰訊會議號：78374132866密碼：2004338:55—9:00會議開幕9:00—10:00報告人：阮立志教授（華中師范大學）標題：消元法與偏微分方程的求解主持人：王焰金教授（廈門大學）10:00—11:00報告人：羅天文教授（華南師范大學）標題：Onmulti-dimensionalrarefactionwaves午休13:30—14:30自由討論11月30日（周四）騰訊會議號：78374132866密碼：2004339:00—10:00報告人：童嘉駿教授（北京大學）標題：GlobalWell-Posednessofthe2-DPeskinProblemunderGeometricConditions主持人：曲鵬教授（復旦大學）10:00—11:00報告人：鄧師瑾教授（上海交通大學）標題：GlobalSolutionof3-DPatlak-Keller-SegalModelwithaCouetteFlowinWholeSpace午休13:30—14:30自由討論12月1日（周五）騰訊會議號：78374132866密碼：2004339:00—10:00報告人：董世杰教授（南方科技大學）標題：CubicDiracequationswithaclassoflargedata主持人：蔡圓研究員（復旦大學）10:00—11:00報告人：袁謙研究員（中國科學院數(shù)學與系統(tǒng)科學研究院）標題：Nonlinearasymptoticstabilityofcompressiblevortexsheetswithviscosityeffects11:00—11:10會議閉幕會議組織：曲鵬（復旦大學）pqu@蔡圓（復旦大學）caiy@

報告摘要報告人：鄧師瑾教授（上海交通大學）標題：GlobalSolutionof3-DPatlak-Keller-SegalModelwithaCouetteFlowinWholeSpace摘要：Weconsiderbothparabolic-ellipticPatlak-Keller-Segelmodelandparabolic-parabolicPatlak-Keller-SegelmodelinthebackgroundofaCouetteflowwithspatialvariablesinR^3.Itisprovedthatforbothparabolic-ellipticandparabolic-paraboliccases,aCouetteflowwithsufficientlylargeamplitudepreventstheblow-upofsolutions.ThisresultistotallydifferentfromeithertheclassicalPatlak-Keller-Segelmodelorthecasewithalargeshearflowandtheperiodicspatialvariablex;forthosetwocases,thesolutionmayblowup.Here,weapplyGreen'sfunctionmethodtocapturethesuppressionofblow-upandprovetheglobalexistenceofthesolutions.Itisajoint-workwithDr.BinbinShiandProf.WeikeWang.報告人：董世杰教授（南方科技大學）標題：CubicDiracequationswithaclassoflargedata摘要：WeareinterestedinmasslesscubicDiracequationsintwoandthreespacedimensions,knownastheSolermodel.Weaimtoshowglobalexistenceandasymptoticbehaviourforthismodelwithaclassoflargeinitialdata.ThisisjointwithKuijieLiandJingyaZhao.報告人：羅天文教授（華南師范大學）標題：Onmulti-dimensionalrarefactionwaves摘要：Westudythetwo-dimensionalacousticalrarefactionwavesundertheirrotationalassumptions.Weprovideanewenergyestimateswithoutlossofderivatives.Wealsogiveadetailedgeometricdescriptionoftherarefactionwavefronts.Asanapplication,weshowthattheRiemannproblemisstructurallystableintheregimeoftwofamiliesofrarefactionwaves.ThisisajointworkwithProf.PinYuinTsinghuaUniverisity.報告人：阮立志教授（華中師范大學）標題：消元法與偏微分方程的求解摘要:我們首先回顧消元法的幾個經(jīng)典實例,然后主要介紹消元法在某些非線性偏微分方程(如輻射Euler方程等)中的應用。報告人：童嘉駿教授（北京大學）標題：GlobalWell-Posednessofthe2-DPeskinProblemunderGeometricConditions摘要：The2-DPeskinproblemdescribescoupledmotionofa1-DclosedelasticstringandtheambientStokesflowintheplane.Itsglobalwell-posednesshasbeenwell-establishedwhentheinitialstringconfigurationisclosetoanequilibrium,whichisanevenly-stretchedcircularconfiguration.Inotherwords,initialshapeofthestringneedstobealmostcircular,andthestringisalmostevenly-stretched.Inthistalk,wepresentsomerecentprogressonpursuingglobalsolutionsforawiderclassofinitialdatum.Wewillshowthatcertaingeometricquantitiesofthestringsatisfyextremumprinciplesanddecayestimates.Asaresult,wecanproveglobalwell-posednesswhentheinitialdatasatisfiesamedium-sizegeometricconditiononthestringshape,whilenoassumptiononthesizeofstretchingisneeded.ThistalkisbasedonajointworkwithDongyiWei.報告人：袁謙教授（中國科學院數(shù)學與系統(tǒng)科學研究院）標題：Nonlinearasymptoticstabilityofcompressiblevortexsheetswithviscosityeffects摘要：Itiswellknownthatthevortexsheetsaregenerallyunstablefortheinviscidflows.Inthistalk,IwillshowthatforthecompressibleisentropicNavier-Stokesequations,thevortexsheetsareonlymeta-stablewiththeviscosityeffects,whiletheassociatedviscouswavesaretime-asymptoticallystableintheL^\inftyspacetosmallinitialperturbations.Also,t