{"title":"气体动力学中的混合行列式、补偿可积性和新的先验估计","authors":"D. Serre","doi":"10.1090/qam/1640","DOIUrl":null,"url":null,"abstract":"We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over \n\n \n \n \n \n S\n y\n m\n \n n\n \n (\n \n R\n \n )\n \n \\mathbf {Sym}_n(\\mathbb {R})\n \n\n. This allows us to establish new a priori estimates for inviscid gases flowing in the whole space \n\n \n \n \n R\n \n d\n \n \\mathbb {R}^d\n \n\n. Notably, we estimate the defect measure (Boltzman equation) or weighted spacial correlations of the velocity field (Euler system). As usual, our bounds involve only the total mass and energy of the flow.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed determinants, compensated integrability, and new a priori estimates in gas dynamics\",\"authors\":\"D. Serre\",\"doi\":\"10.1090/qam/1640\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over \\n\\n \\n \\n \\n \\n S\\n y\\n m\\n \\n n\\n \\n (\\n \\n R\\n \\n )\\n \\n \\\\mathbf {Sym}_n(\\\\mathbb {R})\\n \\n\\n. This allows us to establish new a priori estimates for inviscid gases flowing in the whole space \\n\\n \\n \\n \\n R\\n \\n d\\n \\n \\\\mathbb {R}^d\\n \\n\\n. Notably, we estimate the defect measure (Boltzman equation) or weighted spacial correlations of the velocity field (Euler system). As usual, our bounds involve only the total mass and energy of the flow.\",\"PeriodicalId\":20964,\"journal\":{\"name\":\"Quarterly of Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-12-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quarterly of Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/qam/1640\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/qam/1640","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
通过利用Sym n(R) \mathbf {Sym}_n(\mathbb {R})上的行列式映射的多重线性,我们扩展了我们最近的补偿可积性理论的范围。这使我们能够对在整个空间R d \mathbb {R}^d中流动的无粘性气体建立新的先验估计。值得注意的是,我们估计了缺陷度量(玻尔兹曼方程)或速度场的加权空间相关性(欧拉系统)。像往常一样,我们的边界只涉及流的总质量和总能量。
Mixed determinants, compensated integrability, and new a priori estimates in gas dynamics
We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over
S
y
m
n
(
R
)
\mathbf {Sym}_n(\mathbb {R})
. This allows us to establish new a priori estimates for inviscid gases flowing in the whole space
R
d
\mathbb {R}^d
. Notably, we estimate the defect measure (Boltzman equation) or weighted spacial correlations of the velocity field (Euler system). As usual, our bounds involve only the total mass and energy of the flow.
期刊介绍:
The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume.
This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.