{"title":"三维可压缩粘性微极流体的爆破判据","authors":"Meiyun Dai , Jinxia Liu , Yinghui Zhang","doi":"10.1016/j.aml.2025.109483","DOIUrl":null,"url":null,"abstract":"<div><div>We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>:</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm of the density is bounded, where <span><math><mi>q</mi></math></span> is a positive constant. Particularly, we succeed in removing the technical condition <span><math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> in Hou and Xu (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109483"},"PeriodicalIF":2.8000,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A blowup criterion for the three-dimensional compressible viscous micropolar fluids\",\"authors\":\"Meiyun Dai , Jinxia Liu , Yinghui Zhang\",\"doi\":\"10.1016/j.aml.2025.109483\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>:</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm of the density is bounded, where <span><math><mi>q</mi></math></span> is a positive constant. Particularly, we succeed in removing the technical condition <span><math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> in Hou and Xu (2024).</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"164 \",\"pages\":\"Article 109483\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-02-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965925000333\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925000333","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
给出了带真空的三维微极流体方程Cauchy问题强解的一个新的爆破判据。当密度的L∞(0,T:Lq)范数是有界的，且q为正常数时，证明了强解或光滑解是全局存在的。特别是，我们成功地去除了Hou and Xu（2024）中的技术条件ρ0∈L1。
A blowup criterion for the three-dimensional compressible viscous micropolar fluids
We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the -norm of the density is bounded, where is a positive constant. Particularly, we succeed in removing the technical condition in Hou and Xu (2024).
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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