一维欧拉液滴模型的局部适定性  

The local well-posedness of 1-D Eulerian droplet model

作　　者：郭嘉敏 魏龙[1] GUO Jiamin;WEI Long(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第4期98-102,共5页Journal of Hangzhou Dianzi University：Natural Sciences

摘　　要：研究一维欧拉液滴模型的解在H s(R)空间中的局部适定性。首先,运用能量方法给出模型的解关于时间的一个先验估计;然后,结合标准的近似解序列的逼近过程得到模型解的存在性;最后,通过Sobolev空间H^(s)(R)中输运方程理论得到模型解的唯一性和稳定性结果。In this paper,the local well-posedness of one-dimensional Eulerian droplet model is studied in H^(s)(R).Firstly,the energy method is used to derive local-in-time a priori estimate of the solution to the model.Then,the existence of the solution for the model is showed with the standard approximation process of solution sequence.Finally,the uniqueness result of the solution for the model is obtained by using the transport equation theory in the Sobolev space H^(s)(R).

关 键 词：欧拉液滴模型 存在性 唯一性 

分 类 号：O175.2[理学—数学]