非等熵情況下氣態(tài)星體的穩(wěn)定性.pdf

1、華中師范大學碩士學位論文非等熵情況下氣態(tài)星體的穩(wěn)定性姓名：謝華朝申請學位級別：碩士專業(yè)：應用數學指導教師：鄧引斌20080501AbstractThemotionoftheselfgravita七ionalgaseousstarscanbedescribedbytheEuler_P。issonequationsItcontainsEulerequati。nsforc。nservationofmaSs，momentumandener融an

2、dP。issonequati。nthroughwhichthegravitati。nalp。tentialisdeterminedbythederlsitydistributionofthegasitself：磯diV(∥)=0，(J|Du)tdiv(∥@u)V尸=一pV圣，(pS)￡diV(PSu)=0，△圣=4丌9p，wherep：p(z，￡)，“=u(z，￡)，S=S(z，￡)，P，夕and垂denotethedensityVel

3、oci‘yen‘。opy，pressure，gravitati。nalc。nstantandgravitationalpotential，respectiVelyHere￡≥0denotesthetime，spacevariablesz∈R3ThepresSuresatis6esthefoll。wingequationofstate：P=A，es，wheretheconstantAwillbenormalizedto1，，y1isthe

4、adiabaticconstantAstrophysicistsareinterestedinthestabilityques七ionThesolutionsandstabilityofEulerPoissonequationsareconcernedwiththeentropyfunctionandadiabaticconstantRecentlym徹【yresultsabouttheeXistenceofsteadysolutiol

5、ls盯eobtained，andsomestabilitvresultsareobtainedfbrisentropicflowAsweknow，therea，renesultsaboutthestabilityfornon—isentropicflowThemainpurposeofthispaperisconcernedwiththenonlinearstabilityofgaseousstarsandtheexistenceofs

6、tationarysolutionsinthenonisentropiccasewhen；72，S(z，￡)isasmoothboundedfunctionFirst，、Ⅳegetthesteadystates甜emmlmlzers“theenergyviaconcentrationcompactnessmethod；thenusingtheVariation2Ll印proach、^regetthestabilityresultsoft