VARIATIONAL DERIVATION OF THE GREEN–NAGHDI格林-纳格迪的变分求导 浅水方程组

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1、JournalofNonlinearMathematicalPhysicsISSN:1402-9251(Print)1776-0852(Online)Journalhomepage:http://www.tandfonline.com/loi/tnmp20VARIATIONALDERIVATIONOFTHEGREEN–NAGHDISHALLOW-WATEREQUATIONSDELIAIONESCU-KRUSETocitethisarticle:DELIAIONESCU-KRUSE(2012)VARIATIONALDERIV

2、ATIONOFTHEGREEN–NAGHDISHALLOW-WATEREQUATIONS,JournalofNonlinearMathematicalPhysics,19:sup1,1-12,DOI:10.1142/S1402925112400013Tolinktothisarticle:https://doi.org/10.1142/S1402925112400013Publishedonline:04Mar2013.SubmityourarticletothisjournalArticleviews:121Citing

3、articles:3ViewcitingarticlesFullTerms&Conditionsofaccessandusecanbefoundathttp://www.tandfonline.com/action/journalInformation?journalCode=tnmp20November23,201211:28WSPC/1402-9251259-JNMP1240001ArticleJournalofNonlinearMathematicalPhysics,Vol.19,Suppl.1(2012)12400

4、01(12pages)
cD.Ionescu-KruseDOI:10.1142/S1402925112400013VARIATIONALDERIVATIONOFTHEGREEN–NAGHDISHALLOW-WATEREQUATIONSDELIAIONESCU-KRUSEInstituteofMathematicsoftheRomanianAcademyResearchUnitNo.6,P.O.Box1-764014700Bucharest,RomaniaDelia.Ionescu@imar.roReceived22Marc

5、h2012Accepted13April2012Published28November2012Weconsiderthetwo-dimensionalirrotationalwater-waveproblemwithafreesurfaceandaflatbottom.Intheshallow-waterregimeandwithoutsmallnessassumptiononthewaveamplitudewederive,byavariationalapproachintheLagrangianformalism,the

6、Green–Naghdiequations(1.1).Thesecondequationin(1.1)isatransportequation,thefreesurfaceisadvectedbythefluidflow.Weshowthatthefirstequationofthesystem(1.1)yieldsthecriticalpointsofanactionfunctionalinthespaceofpathswithfixedendpoints,withintheLagrangianformalism.Keyword

7、s:Green–Naghdiequations;shallow-waterwaves;variationalmethods.MathematicsSubjectClassification2000:76B15,70G75,76M301.IntroductionTheGreen–Naghdiequations[14]modelshallow-waterwaveswhoseamplitudeisnotneces-sarilysmallandrepresentahigher-ordercorrectiontotheclassica

8、lshallow-waterequations.Theshallow-waterregimeischaracterizedbytheundisturbedwaterdepthh0beingmuchsmallerthanthehorizontalwavelengthλ.TheGreen–Naghdiequ