{"title":"流体-粒子相互作用模型流态平稳解的全局存在性和唯一性","authors":"Lin Zheng, Shu Wang","doi":"10.1007/s10473-024-0513-4","DOIUrl":null,"url":null,"abstract":"<p>This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in ℝ<sup>3</sup>. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in <i>H</i><sup>3</sup> of the system are established by using the careful energy method.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"37 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime\",\"authors\":\"Lin Zheng, Shu Wang\",\"doi\":\"10.1007/s10473-024-0513-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in ℝ<sup>3</sup>. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in <i>H</i><sup>3</sup> of the system are established by using the careful energy method.</p>\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":\"37 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10473-024-0513-4\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0513-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime
This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in ℝ3. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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