{"title":"线性速度场平面气体崩溃","authors":"Юлия Валерьевна Юлмухаметова","doi":"10.21538/0134-4889-2023-29-2-207-216","DOIUrl":null,"url":null,"abstract":"In this paper we consider a submodel of the gas with a linear velocity field. It is formed by a system of nonlinear differential equations with initial data. Several first integrals of the system are obtained. As a result the order of the system is reduced. For special initial data of the problem, an approximate solution of differential equations of the submodel is obtained. Such solutions correspond to world lines describing the radial expansion of the gas particles from the vortex. Trajectories of motion of gas particles are constructed.","PeriodicalId":44555,"journal":{"name":"Trudy Instituta Matematiki i Mekhaniki UrO RAN","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Плоский коллапс газа с линейным полем скоростей\",\"authors\":\"Юлия Валерьевна Юлмухаметова\",\"doi\":\"10.21538/0134-4889-2023-29-2-207-216\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider a submodel of the gas with a linear velocity field. It is formed by a system of nonlinear differential equations with initial data. Several first integrals of the system are obtained. As a result the order of the system is reduced. For special initial data of the problem, an approximate solution of differential equations of the submodel is obtained. Such solutions correspond to world lines describing the radial expansion of the gas particles from the vortex. Trajectories of motion of gas particles are constructed.\",\"PeriodicalId\":44555,\"journal\":{\"name\":\"Trudy Instituta Matematiki i Mekhaniki UrO RAN\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Trudy Instituta Matematiki i Mekhaniki UrO RAN\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21538/0134-4889-2023-29-2-207-216\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Trudy Instituta Matematiki i Mekhaniki UrO RAN","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21538/0134-4889-2023-29-2-207-216","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
In this paper we consider a submodel of the gas with a linear velocity field. It is formed by a system of nonlinear differential equations with initial data. Several first integrals of the system are obtained. As a result the order of the system is reduced. For special initial data of the problem, an approximate solution of differential equations of the submodel is obtained. Such solutions correspond to world lines describing the radial expansion of the gas particles from the vortex. Trajectories of motion of gas particles are constructed.
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