三维超流动无粘性模型的局部时间解析解

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-14 DOI:arxiv-2409.09404

Pranava Chaitanya Jayanti

{"title":"三维超流动无粘性模型的局部时间解析解","authors":"Pranava Chaitanya Jayanti","doi":"arxiv-2409.09404","DOIUrl":null,"url":null,"abstract":"We address the existence of solutions for the inviscid version of the\nHall-Vinen-Bekharevich-Khalatnikov equations in 3D, a macro-scale model of\nsuperfluidity. This system couples the incompressible Euler equations for the\nnormal fluid and superfluid using a nonlinear mutual friction term that acts\nonly at points of non-zero superfluid vorticity. In the first rigorous study of\nthe inviscid HVBK system, we construct a unique local-in-time solution that is\nanalytic in time and space.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local-in-time analytic solutions for an inviscid model of superfluidity in 3D\",\"authors\":\"Pranava Chaitanya Jayanti\",\"doi\":\"arxiv-2409.09404\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We address the existence of solutions for the inviscid version of the\\nHall-Vinen-Bekharevich-Khalatnikov equations in 3D, a macro-scale model of\\nsuperfluidity. This system couples the incompressible Euler equations for the\\nnormal fluid and superfluid using a nonlinear mutual friction term that acts\\nonly at points of non-zero superfluid vorticity. In the first rigorous study of\\nthe inviscid HVBK system, we construct a unique local-in-time solution that is\\nanalytic in time and space.\",\"PeriodicalId\":501165,\"journal\":{\"name\":\"arXiv - MATH - Analysis of PDEs\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09404\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09404","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了三维空间中无粘性版本的霍尔-维宁-贝卡雷维奇-哈拉特尼科夫方程的解的存在性，这是一个宏观尺度的超流体模型。该系统使用非线性相互摩擦项将正常流体和超流体的不可压缩欧拉方程耦合在一起，该摩擦项仅作用于非零超流体涡度点。在对不粘性 HVBK 系统的首次严格研究中，我们构建了一个唯一的局部时间解，它在时间和空间上都是解析的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Local-in-time analytic solutions for an inviscid model of superfluidity in 3D

We address the existence of solutions for the inviscid version of the Hall-Vinen-Bekharevich-Khalatnikov equations in 3D, a macro-scale model of superfluidity. This system couples the incompressible Euler equations for the normal fluid and superfluid using a nonlinear mutual friction term that acts only at points of non-zero superfluid vorticity. In the first rigorous study of the inviscid HVBK system, we construct a unique local-in-time solution that is analytic in time and space.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Analysis of PDEs

自引率

0.00%

发文量