摘要
Inthispaper,weinvestigatetheRayleigh-Taylorinstabilityproblemfortwocompressible,immiscible,inviscidflowsrotatingwithaconstantangularvelocity,andevolvingwithafreeinterfaceinthepresenceofauniformgravitationalfield.FirstweconstructtheRayleigh-Taylorsteady-statesolutionswithadenserfluidlyingabovethefreeinterfacewiththesecondfluid,thenweturntoananalysisoftheequationsobtainedfromlinearizationaroundsuchasteadystate.Inthepresenceofuniformrotation,thereisnonaturalvariationalframeworkforconstructinggrowingmodesolutionstothelinearizedproblem.Usingthegeneralmethodofstudyingafamilyofmodifiedvariationalproblemsintroducedin[1],weconstructnormalmodesolutionsthatgrowexponentiallyintimewithratelikeet■whereξisthespatialfrequencyofthenormalmodeandtheconstantcdependsonsomephysicalparametersofthetwolayerfluids.AFouriersynthesisofthesenormalmodesolutionsallowsustoconstructsolutionsthatgrowarbitrarilyquicklyintheSobolevspaceH~k,andleadstoanill-posednessresultforthelinearizedproblem.Moreover,fromtheanalysisweseethatrotationdiminishesthegrowthofinstability.Usingthepathologicalsolutions,wethendemonstratetheill-posednessfortheoriginalnon-linearprobleminsomesense.
出版日期
2015年06月16日（中国期刊网平台首次上网日期，不代表论文的发表时间）
